Welcome to the forums!
hopefully this addresses what you were looking for...
Dynasty league: you keep a large portion (or all) of your roster from year to year, usually including a minor league system and a very short major and minor league draft every year to fill holes.
Keeper: you keep a set number of players every year. the number of players you keep and the length you can keep them will vary from league to league. all players that aren't kept go back into the draft.
Roto : your year long totals in each of 10 categories are totaled and compared to everyone else's totals in the league. you get points based on how you place in each category. (for example, in a 12 team league, having the highest home run total would be worth 12 pts, second highest 11 pts, and so on down to the lowest HR total getting 1 pt.) your points for all 10 categories are added up to see who wins the league.
5x5: standard league categories. AVG, Runs, HR, RBI, SB for hitting and Wins ERA WHIP SVs Ks for pitching.
4x4: never played one but i believe it's the same as 5x5 without runs and Ks.
As you get more familiar with the game, you'll want to try leagues with more teams and deeper rosters. 8 team leagues tend to be incredibly shallow, which means that almost everyone has only very good players on their team. as the player pool increases, it puts more emphasis on finding sleepers (undervalued players) and managing the waiver wire in order to win your league.
feel free to ask any other questions you might have.