Rider Cards

I use them to level up other servants, or in some cases just leave them for later.
If you have servants from other classes that you use, I suggest you use up your Rider cards to level them. There's no need to level up servants that you won't use, until those that you will are maxed out.
In some cases it's also good to just store them for later. If you know that you will roll for Jalter for example, you can store up on exp cards, so that when you get her, you can level her faster. And even if you don't get her, you will probably get one or two 4 star servants to level up.

Use them to level up another rider
Always have multiple servants for each classes, you'll need them for hard contents. Even if you won't use them soon, just level them up. Hard contents like Nero Fest will require variation of servants to make your life easier. Later singularities will turn annoying as hell, like a certain boss in Camelot actually demands you to use a full archer team to beat, or a certain boss in Babylonia who is has complete immunity to servants with specific yet common traits. Having more servants ready in your roster will help you more than you'd think it is a waste

For the servants you should raise, I'll call for Georgios and Ushi
Georgios is a very good tank, he has 3 turns taunt, meaning he can give you 3 free turns if you handles him right
Ushi is, a very amazing fighter that could also work as a support, similar to Caesar. I'll say that at the moment she is the best rider you can get for a boss killer, even among the 5*

Also don't ever count 3* and below out, some of them actually worth more than 5*, let alone 4* lmao.

EDIT: I don't think there is any rider who fits art teams very well in both NA and JP since most riders are usually quick or buster based (mostly quick since they abuse stars the most out of all the servants classes, rivaled only by archers), so, I couldn't give you a perfect suggestion about this matter, sorry for that. But you can always try quick teams. CA Hassan and Andersen can feed your rider stars pretty well.

Keep your cards till your inventory is full. Then, you can decide if you need to power up another Rider Servant like suggested by fooming or another Class. You may get Cu Alter or Jeanne Alter...

For your Arts Team, Ushi, Georgios and Francis Drake have 2 Arts Card (3 with Georgios' NP) so you should not have a problem to form Arts Chain.

Ushi (great ST NP) and Georgios (3 turns taunt tank) are a must to get lvl 70, Teach has a Nice np+attack buff similar to Drake, Alexander will be the only Quick support (quick aoe buff) unless you have Atalante, Boudica is bad but pretty so waifu reasons there.