Please correct me immediately if I've understood wrong, but I get the picture that you're not the most computer savvy player? If that's the case, let me explain some basics.
I believe your 17" monitor has been the key for you being able to play this game, because its resolution is so low. A 17" CRT usually worked best at 1024x768, a TFT of the same size 1024x1280. If you do the multiplication and compare it to the current mainstream 1920x1080. Your monitor only needs to draw less than two thirds of the pixel count of a Full HD monitor which is much easier for your computer. For speed, it doesn't matter how large your monitor is, the pixel count is what matters. Thus a 65" television will stress your video card exactly as much as a 15.4" laptop screen if both run at 1920x1080.
An AMD R290 should be able to run this game with most settings enabled. When buying a new monitor, you can choose from two different product lines, both of which will improve your gaming experience. You can choose a higher resolution which will give you a more detailed picture, or you can choose a 144 Hz one which is able to make the motion even more realistic. Way back then it was a common belief that anything above 30 FPS would fool the eye enough for a fluidly moving picture. That is still true for movies, but in today's fast paced realistic looking games even 60 Hz can seem jerky. Then again, if your video card isn't up to the task, it'd be better to have a stable 60 FPS than something bouncing between 44 and 144. The R290 should be able to run the current AH at both alternatives without issues, though, and even the upcoming AH3 which has been said to be more video card dependent.
Lately there has been talk about which processor line to choose. Again, there's more than one right answer. If your purpose is playing only, a cheaper processor with a high clock rate should be enough. But if you'd like to stream your playing in real time, or record your playing with a third party program, you'd need something more powerful. Thus a Pentium G3258 overclocked can run games almost equally well as the i5-4690K or the i7-4790K despite its two-digit price tag. But if you're into sharing your gaming experience in real time, you'd probably need the more expensive versions. Good thing is, they all can be seated on the same motherboard, giving you the opportunity to start with a budget build and upgrade if needed.
