Be sure to get a low profile one with the included mounting bracket. Mine came with two brackets. Here's one within your budget: http://www.amazon.com/HIS-Radeon-128bit-Express-9H657HS.... It comes with an extra low profile bracket. It should work with your acer power supply. Newegg has it for less, but my newegg links aren't working today.
For $50 this is the best video card that you will get and it's low profile so it will fit your computer case. Your best bet is to look at the minimum requirements of the games you want to play and see if this card is in the mix. Here is a video chart so you can see where this card is and what other cards are around it so when you look at the minimum spec's you will be able to tell if this card is in the mix.
You would have to determine if the lag your experiencing is because of your network connection or the video card and one way to find out is to play the single player mode of the game where your not going online to play. A video card will not get rid of lag that is from your internet connection.
If what you have now is intergrated video then the addition of a video card will give you better performance. Here are the spec's of the Pc that you have and the one thing that's going to throw a wrench into the whole thing is the power supply.
220w. The video card that I listed requires a 300w power supply to be in your computer and I don't know if the 220w is going to be close enough to the requirements to run the card. The one thing to consider is that card makers will usually say a higher wattage then what's actually needed to give themselves a cushion.