I need to find a way to get health back without focusing to highly on restoration or alchemy, the only solution I have for this on the top of my head would be to level speech (which I will be) and purchase potions I find along the way, this could add to the challenge of combat. Any other suggestions?

You'll find plenty of health potions in dungeons and whatnot. I have yet to actually purchase any and I do just fine.

I played my first character as a warrior and used alchemy strictly for healing potions, however as previously stated, you will still find plenty of healing potions out in the world. Also despite what Bethesda said leading up to release date, the auto healing rate is quite fast, so much so that on every character I've had, I've resorted to console commands to slow it to a literal crawl.

Fortify healing rate & life steal enchantments are a very quick way of getting your health back. Couple this with lady stone and you shouldn't need any health potion or restoration at all, except for the occaisional battle with ancient dragons.

I use only potions I buy or find for combat use. Between combat I use the base restoration spell I had from the beginning of the game. I put one point into restoration only to cast that spell for half magicka. I've put no points into Magicka. I find this to be a fair balance. I don't make alchemy potions because I did that on my assassin and found it to be overpowered. It's also nice not to have to collect every plant and bug I see this time around.

Once you warrior levels up and gets better you won't even need health potions that much.
In the mean time just use what you find and if you really need to buy some.