It should be noted that being Free-2-Play in no way, shape, or form inhibits you from being able to play competitive TF2, however many communities would prefer for you to be a premium player (and I think either UGC or ETF2L may require premium? Not sure on that). This only costs a mere $5 to be spent in the Mann Co. Store, so it shouldn't really be much. Just grab a taunt or a couple of keys and get yourself some nice hats or something.
The only real differences between the two is that premium players have much more backpack space, can trade items that they get from the drops, can play the in-game competitive matchmaking, can find hats in drops, can send gifts to players, and can craft hats. Some servers also block F2Ps from connecting.
Overall, as far as I know, you can be LFT as a F2P all you want, I've never known a team leader to deny a player solely because they aren't premium.