Upgrading GeForce 9200 & power supply, need advice

I have an Acer Aspire x1200 with a GeForce 9200, 220 watt power supply, and a compact case.

The computer has 1 PCI-E slot available (x16, I think) and it LOOKS like it is a standard length (and could therefore take a standard card?), but I'm not familiar enough with hardware to be able to say so with confidence. My research seems to indicate most compact cases require low-profile cards, but those seem to be smaller than usual and I'm concerned about them being an inappropriate size for the slot, so I'm really not sure if I should be looking for low-profile or standard. The case definitely does seem cramped for space.

Additionally, as the case is small, I don't know what sort of power supply I ought to be considering. Are there special sizes and requirements for what kind of power supplies can work with certain cases/computers?

- 4GB of Ram (the max capacity for this computer.)
- Dualcore AMD Athlon 4850e, 2500 MHz
- 1366 x 768 screen resolution
- No overclocking

I want to improve my gaming capabilities. Yes, I'm aware that the nature of compact computers/low profile graphics cards means that I won't be playing the latest games on high quality, but I'd like the games I currently have to run faster and more smoothly with higher quality.

The games listed below already work on my computer on lower settings; I would just like them to work better, and perhaps increase the life of my machine by opening up some newer games to me as well. Some examples I'd like an upgrade to achieve:
- Civilization 5 at max quality.
- Star Wars: The Old Republic at max quality.
- Skyrim at max, ideally, but acceptable in midrange as well.
- Sims 3 and all expansions at max quality.

I have a max budget of $400, but the lower I can go, the better. Any website that ships to (or is based in) Canada is ideal, but the US is also acceptable.

I don't have any cards and power supplies in mind currently because I honestly don't know how to tell what my computer can handle. The only topics I could find regarding my specific situation are a couple years old and I'm hoping to get more modern advice. Thanks for your time and assistance!

Recommendations for an upgraded, compatible card and power supply will be most appreciated.