No, don't rely on MGE. It can be good for working on your prediction and shit initially, but later on probably it is best just for warming up.
From pub to comp, the transition is daunting.
I would recommend playing on a server with higher-quality players. I personally play on TF2Newbs #3 - 24/7 badwater. Provided it's the right time of day, there will be decent players in abundance.
Depending on the format you're trying to get into, find relevant demos or casted matches and watch them. Watch multiple. Try to get an idea of the game.
After that, I would recommend tf2lobby. Just hop in, try to get a feel for the format. But don't rely on it.
When you feel you're ready, advertise looking for an entry-level team or form one of your own from dedicated people that all get along and are willing to put forth effort.