What you mean by remote areas? It's not like you'll be traveling in Siberia by foot, right? Other way you'll be fine, just make sure to get Russian sim-card so you always have internet. It always helps.

Well north of the Trans-siberian line. From West to East . It's going to take months as it's around 10,000 km..Minibusses, trains, and whatever else I can get.

Thanks for the tip about the sim-card.. Is there a best value sim I should get? One with Data I would hope?

OP, if you haven't already made up your mind, can you break your journey? If so, stop at Irkutsk. And take a couple of days to get to Alhan island in Baikal lake. I was there in 2005 so likely a lot has changed but that was one of the highlights of the trans-siberian for me.

Hei - you just need a letter of invitation for your whole trip not for each hotel - best I've found is at https://russianvisa.top/ .
If you are travelling to Beijing you are not travelling on the Trans Siberian (which goes to Vladivostok) you are travelling on the Trans Mongolian (which goes to Beijing).
When you apply for visa they need an outline of your journey (this will be covered in your Letter of Invitation)- this will include how you will enter Russia (eg a flight from Oslo to Moscow) and how you will leave Russia (e.g. train into Mongolia). Generally you do not have to provide copies of air tickets / train tickets just details of proposed dates.
I always suggest on your visa application you give yourself a few days each way, eg if you intend to enter Russia on 3 July you state 1 July, if you intend to leave Russia on 10 July you put 13 July. This covers you if an delays etc.

I think the good people here have covered most of your questions for a conventional visit to Russia.

One thing that always gets me about Russia is Moscow. It's an interesting place, but by visiting Moscow alone, or basing your view of the country on your experience of Moscow, I don't really think you're seeing the 'real' Russia. It's just like visiting London: interesting city, but it doesn't give you much feeling for what England is at all. As Paul Theroux says, 'A capital city should be the last city you visit in a country, not the first'. I personally have never warmed to Moscow very much, though it has improved a lot in recent years. Saint Petersburg is a more likeable place (apart from the climate), but it was always modelled as a European city and is a visual anomaly. I should say on the other hand that despite its huge size, Russia is a very, very centralised country and that everything of political, cultural and economic importance (apart from the extraction of raw materials) happens in Moscow and St Petersburg. If it's museums, theatre, art exhibitions etc. you want to see, then you'll want to base yourself here.

I fell in love with Russia when I first visited in 2007, and have been going back regularly ever since. I fell in love with the people and landscapes, less so the cities. I travel in my own vehicle, which makes things easier. I've visited all but three of Russia's regions. Western European Russia is not a place of dramatic landscapes, but there are some very scenic locations; the beautiful 'Saviour on the Nerl' Church in Bogolyubovo (just outside Vladimir), or the shores of Lake Nero around Rostov. Also Suzdal as was mentioned above, and some of the crumbling small towns around there. This is also Russia's cultural heartland (although Kyiv is in fact the origin of Russian Orthodox tradition, when the Byzantines first brought Christianity to pagan Rus' in the tenth century) and an easy place to access. Yaroslavl, Vladimir, Kostroma are good options to visit here.

The Volga River is something like the backbone of European Russia; Kazan is worth seeing, and there are cultural attractions at Sviyazhsk and Bolgar. Russian's write-off many of the cities on the Volga such as Samara, Tolyatti, Ulyanovsk as being grim and industrial, but I really love the area around them and the Volga has a certain magic about it.

If you are heading north, Novgorod is just about the oldest city in Russia, and worth seeing. Further north, Karelia and Murmansk region have some very beautiful landscapes indeed, but they are fairly sparsely populated and a dead-end unless you plan to continue into Finland or Norway.

If you want to head west, then Pskov and Smolensk are lovely, though in general the western border regions of Russia are not very interesting.

Heading south, you pass into Russia's fertile black soil region; the land of the old feudal estates. Many of Russia's celebrated writers and poets had estates here, which are now museums. Further to the south is the Don Region and beyond that the Caucasus Mountains; unquestionably the most dramatic landscapes in European Russia. Culturally they are fascinating, but probably not what I would recommend as a first glimpse of Russia.

You could also be more unorthodox and base your first trip in Siberia or the Far East. Here it's much more about the landscapes than history or culture and the republics of southern Siberia (Altai, Khakassia, Tuva, Buryatia) have some of Eurasia's finest scenery. The people of Siberia are famous for being friendly and extremely kind (not that Russians in the west aren't) and you'll easily make friends if you stay in a place for a while. But here it really pays to have your own transport as the cities are often not very interesting. Exceptions in my opinion would be Irkutsk, Tomsk and Vladivostok. Every now and again however, one finds an idyllic place such as Verkhoturye in Sverdlovsk Region, or Severobaikalsk at the north of Lake Baikal; even far-flung Magadan was a highlight (very personal choices obviously). You could base yourself in one place such as this, make some local friends and learn far more about Russian people and culture than by rushing around between cities on an itinerary. The language barrier may be a problem here: you could use Couchsurfing to meet local English speakers.

I hope this has given you a bit more of an idea of the dizzying number of options out there, but want mostly to say that there is far, far more to Russia than the two big cities.

EO

Hi firstly you are not planning to travel on Trans Siberian - you plan to travel on the Trans Mongolian; the Trans Siberian goes to Vladivostok not Beijing.
In regard to Real Russia we have used this agency a few times and have nothing but praise for them they are very helpful and competent; of course they charge a fee so you need to weigh that up against doing it all yourself. (As far as costs). You will need a Letter of Invitation for Russia and Mongolia Real Russia will prob give you these for free if you book other travel through them; these are another cost to consider.
Yes you can do it all yourself, ie get visas book train travel, get Letters of Invitation etc - it just takes time but as you are not going until Sept you have the time.
Re booking hotels in advance - this is not 100% true, what you need is a Letter of Invitation (LoI) which shows your intended route / mode of travel and cities where you will stay and hotels. However this is flexible, no one actually checks that you ended up staying at XYZ hotel in Moscow on the 10th of whenever. What we have done is selected some hotels on say booking.com (found ones that allow you to book and cancel without paying fees)and used these on LoI so have some sort of plan to present to get visa.
As far as what cities to visit well that's up to you really - St Petersburg to Beijing is crossing more than half the world, a lot of cities there. I suggest you do some research of cities on the train route and see what appeals, the only must go place to me is Irkutsk.
flumy has given some great advise above also.

So are you travelling alone or with someone else? You post is a bit confusing. I can only base on my own experiences in Russia including travelling on Trans Siberian last year, I found generally Russia to be a safe place to travel. People are friendly and I've found very hospitable Have met a few female western travellers who are travelling alone and no problems. Russia is a very diverse country as far as race - I have not seen any evidence of the "lot of racisim" you state - not sure what your source is for this statement. Don't think the average Russian dislikes Americans, I would say they are a lot more tolerant than the average American is of Russians. All in all I don't think your concerns are justified and I'm sure you'll have a great trip.

In the big cities along the Trans-Siberian rail line (e.g.: Vladivostok, Irkutsk, Novosibirsk, etc.), is it easy to find internet cafés and/or internet centres in so-called business hotels, or not?

I understand what you are saying: if you have a web-enabled device such as a smartphone but access to the web is 'weak' where you are, it is not going to help you... Mind you, in Britain, you have parts of the country where broadband is very slow or non-existent, from what I have read, and I know of places where mobile phones do not work at all (no signal) -- and that's not in the middle of nowhere but on the edge of a town in Wales!