I've decided to play Morrowind again, but this time without console cheats. However, it seems to be really difficult making loads of septims as a lvl 1. Anybody know how to make some fast cash?

(My character is not a very good theif, so i would prefer money making techniques that don't involve stealing or pickpocketing)

You do not need to be good at stealing because you can do it anyway, unless you are roleplaying a good guy. You can simply travel to Caldera where you can visit Ghorak Manor. There are a few crates that you can find upstairs. They contain different pieces of orcish armour and you can grab all of them freely. The orcs might shout at you but they will not attack. Furthermore, you can sell the armour for its full price to the Creeper. He is a unique merchant which looks like a scamp. You do not even need to find him because he is chilling in the same place upstairs

Well I'm roleplaying as a guy who kindof walks down the middle path of moral good and bad, or more like "doesn't steal from the living, but loots the dead" kind of guy.

soul trap some random low level creatures, you can get free unfilled gems at the mages guild once you joing. They sell for tons of drakes, plus you get in some practice with weapons and mysticism

In that case I suggest pearl diving. Just stay close to the shore and ignore tombs that you might see. However, you could try clearing the nearest tomb due to its weak guards and a very valuable reward. The tomb is located at north from Seyda Need, next to the shore. You will probably need some of Arrille's equipment though. Two fire magic scrolls, good versus enemies that resist normal weapon, should be enough. You should be able to get them if you solve Fargoth's quests first. If not, you can always do the quest about the absence of the tax guy. Good luck