Madagascar is an inexpensive country, once you're there. I was positively surprised by the hotels we stayed at, each one had wifi that functioned to some degree, running water and electricity for at least part of the day. Hotels normally cost in the region of €30-40 per night (I am pretty sure that is per room). Meals normally cost less than €5, a bit more in Tana.
Due to inexperience and lack of time, I travelled with a group, which turned out to be a good choice, both from a social perspective (I was travelling solo), and because of the amount of things we packed into our two weeks. We came across numerous groups of varying sizes that had decided to hire a driver and a 4x4, which would have cost roughly the same if travelling with someone else. I think I would have found that a little boring, considering drivers like everyone else there probably speak very little English (our guide instead had good English, which allowed us to get under the skin of the country a bit, and understand their system of beliefs and traditions which is extremely interesting).
As for travelling independently, it appears to be very difficult as the only means of transportation are taxi brousse, which can be sporadic and only leave when full. The language barrier comes into play here as well. We came across someone that had attempted to travel this way, and she soon had to give up and hire a 4x4. You have to bear in mind that a lot of what is worth seeing there is quite remote and far away from the cities, so even if travelling from one city to the other wasn't a problem, you'd still have to arrange your trip into the natural parks and relative transfers (guides are mandatory to go into natural parks).
I would also add that it's a massive country with extremely poor infrastructure, which makes for relatively long drives as it is, without the extra difficulty of catching taxi brousse and having to organize everything yourself, especially considered that you only have three weeks to spend there.
In terms of itinerary, this is the one we followed: http://bit.ly/1tUGZMi
It roughly follows the Route National 7, which is quite popular and one of the few decent roads in the country by the looks of it.
We left Tana immediately, drove to Ambositra the first day and trekked to a Zafimaniry village the following day; they are extremely capable wood carvers, it was really interesting and at the same time humbling to see the simple way in which they live.
Then we drove to Ranomafana, which has a totally different environment, almost rainy forest-like. There is a natural park there, one of the oldest in Madagascar, which we visited at night and early in the morning. We got to see quite a lot of wildlife, including chameleons, frogs, hawks and several types of lemurs, some extremely close.
The following day we drove to Ambalavao, from where we set off for a four-day trek into Andringitra National Park. I am not sure if you are into trekking, but the park is absolutely stunning. It is extremely remote, mostly empty and has a great primordial feel to it. It was probably the highlight of the trip for me, it really felt like one had escaped from the world.
After one night in Ranohira, we visited Isalo National Park, where we camped for two nights. This park is more mainstream and more visited, but equally stunning, with lunar landscapes and natural swimming pools in the canyons. Interesting wildlife too.
Finally, after a brief stop in Tulear, we drove to Ifaty, where we stayed at the beach for two nights. The road stops at Tulear, it's all sand tracks along the coast. We visited a spiny forest park, where we saw lots of baobabs and other extremely unusual plants. The sea in that area is wonderful, and would definitely recommend a few days of laziness at the beach and perhaps some snorkeling. We stayed at the Hotel La Plage, which I would recommend; it's very reasonable and has bungalows by the beach. The beach is open to locals that use it to get from one village to the next, so while the hotel is gated, it really does not alienate the locals or prevent interaction.
We then flew back to Tana from Tulear. Other hotels I can recommend are Belvedere in Tana, and L'Artisan in Ambositra. Other smaller cities have only a handful of hotels anyway.
Sorry for the long message, Madagascar is a stunning country with even more wonderful people, I am sure you will enjoy it.
