I just had that exact same issue to think about. I decided to go 'Hard Mode' by starting in Frost, I couldn't leave town for a LONG time. What I did was set myself up for self-sustaining by focusing on food acquisition, AKA Forage/Hunt. After a while your starting slave levels, you just have to hope you can meet the level up requirements. After getting their >Agility< up a bit, you should be able to avoid fights as long as she's in your battle group. Once you can, just head out, and go to Wimborn to fight 'easy' enemies. And, since you're upping their agility, you can buy a longsword from Frost to make sure they can fight at their best.
The steps I used to get out of Frost:
1) Forage/Hunt to keep food at a sustainable level.
2) If you get enough excess food, set them up as a lumberer for money. Note: If they're not good at the job, they won't make much, but you do slowly build a bit, which can be used on rope, for later, a long sword for your slave, or buying a slave to give you a bit more fighting power.
3) Save before leaving the town to check if you have enough agility to avoid the bandits, which are the hardest things to get away from near Frostford.
4) Head through the Marsh, Far Eerie Forest, Shaliq, Forest, and Wimborn Outskirts to arrive at Wimborn. Buy armor, if you can, for later, can't equip it now. Or, alternatively, buy teleport stone for 500 if you have some pocket change, for easy travel.
5) Success! You've escaped the danger zone! Good luck with the rest.
The wiki link'll help with the slime issue.