1

You can start the process before leaving home. Contact various agencies and start from there. Train tickets only go on sale 10 days before so some things cant be done till last minute.
If you want to go outside Lhasa, then that needs to be done prior as the agency will need all info to apply for the TTP.

2

I agree with #1.
Another way to go, since you seem to have a lot of time, is to go to Xining and find an agency. It will take a few days to get your train tickets. But, again, its best if you make all arrangements from home and avoid any surprises. As for the train ride you need to plan it well. What type of seat do you want? I went with a soft seat, middle bunk. This is more expensive but certainly more comfortable for the 24 hour ride.

3

We went soft sleeper because those were the only tickets our travel agency could get on the black market.
I'd not be signing any contract either until I'd read every single word and made sure all the i's were dotted and all the t's crossed.
We went prior to the restrictions but still needed to prearrange a trip to EBC and back. Everything had to be detailed in these contracts and drivers stuck to them. It wasnt uncommon for clients to come unstuck when they wanted to deviate from arrangements made in contracts.

4

You can arrive in Xining and then plan your trip to Tibet, but you will most likely need to spend between 7 to 10 days there (at least) in order to give the travel agency enough time to arrange your trip and purchase your train tickets. Train tickets to Lhasa are extremely difficult to get during the high season (June through mid-October). Travel agencies normally need to purchase these tickets 10 days before departure. For this reason, most people prefer to start arranging their Tibet tour in advance, so they minimize the amount of waiting time.

I recommend using a Tibetan owned agency based in Xining and start arranging your tour in advance. All travel arrangements for Tibet can be made through email. Read the following links for more about how to travel in Tibet:

Travel in Tibet
How to arrange travel in Tibet

5

I recommend to contact an agency based in Xining to settle down everything before you arrive Xining. But if you have some plans in Amdo(Qinghai) region, then you can sort it out while you are doing some travels around Xining. The train tickets can be difficult to purchase in July and travel agencies need sometime to prepare the best way to purchase your tickets. As it is now, you have to have your permits to get train tickets in some of the cities in mainland China. If this keeps all the way to July, then you definitely need to book a tour with Agency at least 12-15days before. Train tickets in July sales on either 5 days or 10 day ahead of your departure time.

6

August is one of the most busiest and expensive season of Tourism in Tibet if we compare to every last year as in August every year there is yogart festival, which is one of the most important and biggest ceremony of festival in Lhasa. This year shoton festival is on 17th August and the festival remains for about a week but still its busy and expensive and if you want to travel Tibet in the bit cheaper time than its better if you can change your travel date to Tibet bit later around July or September will be good but if you cannot then you can contact a travel agency to give you the cheapest price as possible for the 7-10 days trip in Tibet, few days in Lhasa and over land trip to Everest base camp and back to Lhasa is a good option then you can let the travel agency excluded your meals and accommodation so that you have option to choose cheaper accommodation or local food to minimize the prices. Many travel agencies in Tibet can help you to get the train ticket to Tibet from Xining but August is very busy season so make sure you book the trip around a month before so that there is lots of time to prepare for permit and train ticket for the travel agency.