If you have upload speed in the 1-2 Mbps (megabits per second) range, you've got a GREAT upload speed.
Download (or downstream) speed is how fast data gets TO you.
Upload (or upstream) speed is how fast data gets AWAY from you (how fast you send data out).
Most folks have between 0.5 and 2.0 Mbps upload, and have anywhere from 2 to 50 Mbps download. As long as you have at least 5/1 (5 Mbps down, 1 Mbps up) you'll be fine.
That's not the whole picture, though. If someone else you're playing with has slower internet, they can't send the data as quick - so it doesn't matter how fast YOU are, the game is limited by the slowest person.
Example: Let's say you drive a Ferrari (=very fast internet). If your friend is coming over to visit, and he only has a bicycle (=slow internet), your Ferrari isn't going to make him get to your house any faster.
The other thing to watch is called Latency. It's the delay between when data is sent and when it is received. Most folks have a "round trip time" (time for a request to get from you, to the other end, and back) in the 50-70 ms (milliseconds; 1/1000th second) range. If you live far away from the data center of your ISP, it can go up to 90 ms or more. 100 ms is 1/10th of a second, so that's a noticeable delay. If you have fast internet and live close to the data center, it can be as low as 30 ms or less.
So really, there's not too much you can do - as it depends on the speed of the internet of ALL the people playing. Sometimes you'll be the fast one, sometimes you'll be the slow one. :(
Getting a faster connection CAN help latency, and can give you an advantage - but for the cost, it's normally not worth it. Doubling your internet connection speed may cost $30-$50 more per month, and may help your win/loss ratio by about 10% - so if you were winning 0.5% of the time, you'd go up to winning 0.55% of the time.
I hope that helps clear things up! My connection is 17/0.75, and my ping (the measurement of latency) is in the 60 ms range. I've never had an issue with my connection being the reason I lose. If you've got more upload and similar ping, I'd say you're in really good shape.