The comps I play are usually based on what champs the game decides to give me, which sometimes will make me end up shafting myself and losing to the broken stuff you mentioned. Idk, I guess I just enjoy trying new synergy combinations and seeing what I can put together, watching my carry champs pop off
The way some people get 3-Star champions fast is through a strategy called hyper rolling. Personally I'm more of an econ player and try to play for a strong mid-late game. It sometimes can beat those with a bunch of 3 stars, sometimes it can't because I lost too much HP early or they have a 3 star Veigar.
My advice would be to learn some of the strategies I've mentioned like hyper rolling, building econ, and scouting. Scouting what your opponents are building is important because you don't want to go for a team comp multiple other people are going for and find yourself struggling to 2-Star an important champion because so many people took them out of the pool. If I see anyone building glacials with or without berserkers I always buy all Olafs I see to make it harder for them to get their Olaf 2 star or get Olaf at all :)
Same goes for any other units that I see people may need. Inferno summoners? Buy Annie.
You see the guy in 1st or 2nd have a Malzahar or Annie with a spatula on their bench and they have mages? Next carousel take that 
if you can because if he gets it, he's going to make them a mage and you're gonna have a bad time when the double tibbers/minions come out.
Or simply don't play TFT if it's not something you enjoy.
