Next Banners?

Next event will be summer event. Basically swimsuit female servants, which are all waifu tier. Gameplay wise, Altria Archer is the best in the summer banner. But since you are F2P, you can skip it and get a welfare archer servant Chloe which is 4 star Altria Archer.

Nero Bride in Nero Fest event is a DPS that can support as well. After that comes the second Jalter banner. Then comes the Halloween event that has Tamamo on rate up. And Merlin comes in a month.

You could check here for the list of servants in their respective rate-ups. http://fate-go.cirnopedia.org/summon.php Just take note that waifu/husband first before gameplay.

You can check expected next event at https://fategrandorder.wikia.com/wiki/Fate/Grand_Order_Wikia next is summer event followed by Camelot pickup banner 2 and Fate/kaleid Prism collaboration event

I have to recommend rolling at least a few rolls on the summer banner. Which comes in 2 banner(one for tamamo and one for altria). The 4 stars on the banner are all excellent pickups. Lancer kiyo,anne bonny and mary archer, rider MOEDRED. Dont even mention lucking out and getting tama lancer. Other banner has the best archer in the game for arts teams and ruler martha who is a offensive buster crit ruler and caster mary ann.

Or you can just roll for memelin near the end of the year.
Seriously Merlin is the most bang for your buck in terms of servant.
Just make sure to save 500 quartz if you wanna guarantee almost 100% chance to get him even with bad gacha E rank luck.
300 quartz is around 50% chance on average to roll a 5 star