how fast does your internet connection need to be for mp?

Not very. The bandwidth used by the vast majority of online games is pretty low. What matters far more is the stability of your connection. However, having higher internet speeds will somewhat reduce the impact that other people or applications have on your gaming experience.

Indeed.

It's also worth noting that the speeds advertised by ISPs are in Megabits per second (Mbps), which is different from Megabytes per second (MBps or MB/s). One Megabyte = 8 Megabits. To get an pretty good idea of what your maximum download speed is, take the Mbps and divide it by 8. For example, on a 30/10 Mbps connection, you can expect to download around 3.75 Megabytes or upload a maximum of 1.25 Megabytes of data every second (real-world numbers will be a bit lower for a number of reasons). The data transfered by online gaming will never put any appreciable strain on your connection provided it wasn't pulled from the depths of the bargain basement.

I run MP with only a 1 Mbps connection and get by ok for the most part.

Usually depends on who you match with for games that determines whether you lag bad or not it seems. Some say I'm a good Host, and others yell at me for it being bad in ME3MP.

512 kb minimum

Better yet - Don't use Wifi at all, if possible.

There is absolutely nothing wrong with properly functioning Wifi.  This is an early 2000s problem, unless you're super far from the router or have stuff in the walls blocking the signal or something.