Regular or Prototype Cu?

Regular Cu is considered to be best lancer (out of 1-3 stars servants) due to his survability and instant death chance on his NP. Prototype has a bit more damage than regular at the cost of survability. It really depends on your situation in the game (main story progress, summoned servants, CE, available support servants from your friends).
I'd go for regular 1st, if after few weeks you'll still suffer from lack of lancer with good damage output you can go for proto without hesitation.

I would take regular Cu over prototype Cu anytime. Just looking it up on youtube, you can see how op regular cu is (he is prob the best solo character in the game so far). His damage is a bit low but later in the game, survivability becomes increasingly important when you can't finish the round in 5 turns like at lower lvls.

If you have just started, dont invest in either of those tho for now.
Normal Cu is a 5 star in disguise, but you can realistically made use of him only when you are alredy at camelot. till thet point any berserker from your friend list will just wipe the challange.
Later on invest on Normal cu.
Cu prototype is nice and have a tad more damage then normal cu, but whats the point in leveling him for the first part of the game anyway?
Pls, the next Free SR servant is a saber. So wait a bit and invest in her if you need a lancer

FSN Cu is better for solo memes. His sheer survivability makes him able to stay out on the field for days.

Cu proto lacks battle continuation and disengage, trading them for a crit damage boost and star gather rate boost (as well as increased damage vs beasts but you probably won't be using that much). So neither one is really better. Cu proto does more damage so long as he has a steady supply of crit stars. But when it comes to soloing stuff, FSN Cu is better.

My cu is lvl90 10/10/10
Cu proto is still lvl70 4/4/4

Have never regretted the choice.

Regular cu for more durability, proto cu for more damage