Moving into a new apartment.
I will have a 2-5 mbps DSL wireless network and a wireless adapter on my console. Will I be able to play Halo Reach and Halo 4 with this? Anyone have experience with this kind of thing? Lag? Delays?
Thank you. 
I have played Reach, H3, with a .725kb DSL, and I now currently run a 3.0mbps DSL and it runs perfectly :P. You will be fine shouldnt have any lag or delays with that speed.
Just incase though, since you are using Wireless, try to disconnect your Laptops, PCs, from the internet if you are in a Matchmaking Game, it can at times cause a interference, but I havent experienced it since I upgraded to 3.0. Just a suggestion :),
Playing on a connection that regularly gets capped (only 15gb a month…) you will be fine. Even at 64kbps you can sort of get away with BTB as long as there isn’t mic spam.