I am not sure if the rounter and adapter will work together, they use to have an adapter for the DGL-4300 but it is not on newegg or tigerdirect, right now.
Also imagining that those two worked together i get them home and connect my cable modem to the router and the adapter to the computer I want the wireless connection on and i can the just connect an ethernet cord from the back of the router to my other computer, right next to the modem and they will both have a connection right? after i install the software and such?
Well I would suggest any atheros chipset that supports super g for that router. I have the DI-634M which has similar specs but better range and cheaper but doesn't have a gigibit switch. Check out cards like trendnet smc on the low end and dlink and netgear on the higher end. I use airnet cards although I think they went out of bussiness which is a shame cause they're dirt cheap and worked well. Just get it confirmed that its an atheros chipset although most things listing 108 mbps are.