Potion spamming is only a low level issue. Once you upgrade your armor and raise health, it's just one or two potions during the tougher fights.
^^^^This.
1. Low levels are tough for pure warrior types. You don't have a lot of health or stamina to really effect a defensive or offensive play style yet. You also don't have good armors, if you are even lucky enough to find a full suit. You don't usually have a good shield or good weapon unless really lucky to find one. And cash is in short supply... So you will be getting thumped a lot at lower levels, until you master your Warrior craft.
2. Use a follower. They can be really useful whether as additional offense, or to serve as a distraction tank. I prefer archer types on my low level guy, but really ANY type can be useful. You can do mini-quest to get Faenal (riverwood?) on your side for nothing, or go to The Bannered Mare in Whiterun and beat Uthgerd in a brawl. Those are two dirt cheap options early.
3. Grab potions when you can. I would suggest doing enough alchemy to make your own health and stamina potions so you can save a few coin over the long haul. Once you know which ingredients make those two potions, you can focus on buying them when available or harvesting them as you roam.
4. Going for Light Armor perks could surely work. While you get less overall armor level, when you master the art of the Warrior- you shouldn't be getting hit all that much. Learning to use shield blocks, how to avoid enemy power attacks, timing and weaving your strikes, these will all result in you taking less full shots to the body so to speak. Light Armor also has a perk for stamina regen. This allows you to either opt for a lower stamina spec, or to be more aggressive in your stamina usage (for those bashes, blocks, and power attacks.) I reiterate, your shield ought to be taking the blows if "ur doin it rite." Perks in Blocking will make it very useful for both defense, and for tactical offense. At higher levels and better armors along with Perks, you can afford to take some hits though. (This is why life at low levels is tough. All the dancing in the world isn't going to help you avoid ALL hits.. and the ones that get through can 2 shot you)
5. Use a bow for ranged attacks. You don't have to go crazy in Perks there. But a few to raise it's damage, or maybe even get you the zoom and slow-down (at least 1 slowdown level) can really help. Since you aren't spending any Perk points in magicks, you ought to be able to spare a few points for Archery.
6. Really make sure you fill out that Blocking Perks. Otherwise archers and mages will rip you a new one. Mages will still be a threat, but you'll at least stand a fighting chance.