I'm in a similar position. I have a cheap belkin USB wifi dongle which I use. I'm not sure if it's worth buying a proper wifi network card. My router isn't brilliant and I have a feeling I would need to upgrade that too.
My answer would be try borrow someone's and try it to see if it works. Sorry I don't have a better solution.
A better card or other wireless option may indeed work better. Or it may not. It may even be worthwhile to get a new router. With wireless there are no guarantees that apply universally, unless you're prepared to spend considerable amounts of money.
If you want something that will be sure to work that is also affordable, you'd need to go with a wired connection. Unfortunately, the viability of this depends on your house construction.