you can join the water rag to leech off it (cause you won't do much til you're WAY stronger), but you can also get SR assault (and defender but probably won't need it) from the other two raids. in ALL raids you do, do one round of attacks (as in hit the attack button) and you're considered "contributing" to the raid. it should give you some chests, but you can honestly get more by getting Vice-MVP and MVP so dish out as much damage as you can when you get strong enough. eventually get strong enough and you can solo the two weaker raids and possibly the rag one (it'll be highly difficult to do so on the rag fight though)
as for N weapons, just set it so those get auto sold. unless you plan on using them as exp fodder, no point in having them clog space. And R weapons... go look at how to properly enhance weapon skill levels to get the most out of those. R weapons are the main "go-to" source for building up skill levels (unless there's something like the union event soon that feeds tons of grails). they can be fused into each other or even other weapons at R and above to boost skill leveling efficiency. the higher your skill levels, the more powerful the grid. base stats can do a lot at the start too so higher rarities are the way to go for weapons to keep.
as for inventory space... it kind of depends. if you don't plan on spending much (if at all), you're better off using magic jewels for the gacha to get more attempts at getting more hime. doesn't matter how much the rates can troll you, free and low cost players NEED the extra pulls. you might need some extensions though when you progress later on so if you feel like you need space for other grids (you will be holding no less than 60 weapons if all 6 elements are optimized) then go extend some space. There's no real need to max out space, but a good 50-100 extra slots can help.
speaking of space, try having your auto sale functions set as follows to help manage it more:
weapons:
Attachment 11733
eidolons:
Attachment 11734
and having your enhancement recommendations set like this will speed up exp leveling for both eidolons and weapons:
Attachment 11735
one last thing, there's periods of the day (forgot which times) when you can farm for more gems. if you want to pull the gem gacha a lot more (which you should cause it feeds a lot of good stuff, including R weapons), do that quest. you even get 2 runs a day you can do at any time. those auto sale functions keep inventory down cause you can get up to 1000 pulls a day from the 10-draw gem gacha alone...