Is there a server where there is a strong natural regen from level 1?
 

I'm looking to try a certain combination of characters and this would help a lot.

Maybe it would help if you provided a bit more context. How many characters do you intend to play? in what era?

I assume there are many servers which offer increased health regeneration at level 1.

EQ Might for example:
- you get a custom charm at level 1 with various stats, one of them being +20 health regeneration
- the HP regeneration cap from items is increased from 15 to 100
- every rank of innate Regneration AA gives 1 instead of 3 HP regeneration, there are 30 ranks.
- there are free buff NPCs available at level 1, which also offer regneration buffs that last 2 hours
- later on there are quests for custom self-only buffs with high regeneration and elixirs with unlimited charges (recast time) to allow most classes to be successful at soloing / duoing