what is the base for? does it generate me money? or just decorations? do i have to pay for the rental?
Bases can boost your damage/healing/power healing. You put up your armories there, which is where you can save your character build, and if you have more than one, you can play both roles (DPS & Tank / DPS & Troll / DPS & Healer, depending on your power). Plus, if you are in a league, your base will grant you prestige once a week when you enter it. If you purchase a teleporter, it will greatly reduce your travel times too. These videos might help you out further.
Real quick right off the top of my head. ...... Hopefully I do not forget anything. Bases have places to put amenities and base items like Armories ( 1 click gear, SP, color, style changing ) Character banks Mail box Teleporter Soda & repair vendor R&D vendor R&D station Sparring dummy Respec station Bases have the mainframe and generator that have upgrades for your characters with things like Colored gear mods White mods Teleporter mods Trinkets Backup Sidekicks. The bases also help you earn ( prestige points ) that you use for other things like Opening a league hall Opening more slots in your league banks Buying league buffs OR......if you just want to geek out and be a decorator you can do that too ( decorating your base adds prestige points ) good reason to geek out all SIMS like LOL ( Prestige points ) Prestige points earned from bases and league halls are based off of base decorations added to bases and league halls. Bases earn prestige points on a weekly basis depending on the number of base items placed in each base that you own. League halls earn a one time prestige point bonus with every item added to the league hall. Items that count towards prestige points are base/league hall items & gear. Hopefully I didn't miss anything & maybe this will help.
Besides what everyone else said, the best thing of the bases is you can make it where you don't have to go to the Watchtower Lagville! Only time I go to the tower now is for a "walkin" mission with the league, if my alt is on a level where I have to go there for equipment, or getting another LPVE character. That alone is worth the bases weight in gold!