Assassin, probably a low-class Assassin mind you but Assassin nonetheless. They've learned a few ninja arts from the Japanese assassin-class servants and actually perform them decently. Magic, swordplay, and such are all rather...bad. I can't think of what they would 'ride' if they were a rider.
Ritsuka is a mecha otaku... or at least in this comic.
They command an army... A moving fortress is perfect fit, no?
There are servants who are willing to build a Gundam or futuristic fortress for them XD
I'm pretty sure Ritsuka also like them flashy. Most rider's NP are like that.
Rider is a safe bet; part of the reason there's so damn many Riders is that for a time it was the dumping ground for "We can't figure out where you go, but you're powerful and you clearly don't go anywhere else, so you're a Rider now."
Ozymandias is a Rider, as an example.
That being said, I personally would say Ritsuka would be a 3-star Caster. You have to remember we are an awful mage; our true power is quite literally Heart(tm), but the Throne doesn't really have a container for that and we are not pure of heart enough to slide into the Ruler class the 'proper' way (only Saints are supposed to be allowed to be Rulers. Yes, I can already hear you typing about Amakusa; He's not supposed to be one, he cheated and forced his way into it in Fate/Apocrypha).
Dante made the offer because he knew Ritsuka would never accept it. The world's Last Avenger might be able to, well, avenge it, but they would be in no position to rebuild it, and that's what we need to be able to do with the bleached world. Avengers are flame and rage and ash, that isn't what fixes a broken world.
we are not pure of heart enough to slide into the Ruler class the 'proper' way (only Saints are supposed to be allowed to be Rulers. Yes, I can already hear you typing about Amakusa; He's not supposed to be one, he cheated and forced his way into it in Fate/Apocrypha).