Overall this is pretty reasonable for a first time player, and you shouldn't feel the need to restart or anything. Only having lost one nation means you aren't even close to defeat yet.
A good indicator that you really are hopelessly behind is losing multiple high-level units, to non-terror missions. I assume you aren't playing on iron-man, so if you can't get through a basic UFO crash without losing your high ranked units you should then consider restarting. If you have multiple decently ranked troops left you can generally recover, especially on normal or easy difficulty.
That said, there is one primary thing to work on in future games, and it is related to the reason you feel constantly broke: Satellites. The most important goal in the early game is to get as many satellites up and running as possible. This is because satellites are your primary source of income (they give a bonus each month), and are reliable sources of panic reduction as well. It's possible to launch as many as 4 satellites in the first month alone, and the "satellite rush" is a popular strategy. That said, I would not try for that so soon, especially since on normal difficulty it is overkill. Instead, in future games try and launch a minimum of 2 satellites per month, for the first several months of the game.
This will give you a strong economic backbone, as well as ensuring panic is at low levels throughout the early game.
With regards to your current game, satellites are going to be valuable as well. However now that you are several months in it may be a bit tough to fit them into your budget.