Overhauling home wifi network, need product suggestions

Hello all!

This is my first post on this forum, it seems like a resourceful place to say the least.

I just got an Xbox 360 and I have it set up in my living room with the HDTV. Now, my wireless router is in another room and my family will not allow me to just run an ethernet cable across the house when I'm on xbox live. So, I purchased the Microsoft wireless adapter for the 360. It does work, but the signal strength of my wifi is not the strongest and the games sometimes lag.

I've decided to upgrade some of the wireless technology in my house to fix this problem.

From DSL Reports, this is my internet speed:
Download Speed "2379 Kb/s"
Upload Speed "417 Kb/s"
Latency 26 ms

I currently own a D-Link DI-624 router. I was thinking of replacing this with something better. I don't want to spend a lot of money, so what is a router that tops this one for less than $100. I've also heard of hacking certain Linksys routers, what's up with this?

In terms of my network, this is what I have going. 1 PC hooked up to router via ethernet, 1 wireless desktop with a POS old Dell USB wireless adapter (definitely replacing), 1 wireless laptop, and the wireless 360. I currently have static IP addresses set up so I can have port forwarding for utorrent (I must maintain this lol).

Finally, I think I need to purchase an access point. One that just plugs into the wall, picks up the wifi signal from the router and then rebroadcasts it to the part of the house where the 360 is. What is a highly rated access point?

I understand that it is kind of obnoxious to just be asking for product recommendations here, but I hope I can get some useful feedback and recommendations.

If you need any further information, like distances between rooms or how many walls there are, etc, please feel free to ask.

Thanks!