Being in debt is a crashing bore. The best advice I can give novices is to pay their debt off as quickly as possible...while in debt, one cannot give coins away, which can be a bit of a bother when someone's selling that oh-so-perfect piece of fluff that you just can't live without. So, without further ado, here is my guide to equipping oneself in the cheapest possible manner.
CONTAINERS -- When you first start out, you have a nice large sack in which to put things. You'll quickly discover that "large" is a misnomer; the bloody sack barely carries anything at all. So, your first priority should be to find a second sack. You can, if you're feeling brave, take a stroll through goblin territory (head West in The Crossing until you find the West Gate, then go through the gate and down the path), where you should find sacks aplenty. No one wants them, but if anyone's in the area it's considered good manners to ask before picking anything up. If you don't wish to go to goblins, just wander around town...people are dropping empty sacks all the time.
Now, two sacks are not really enough once you get going, but they'll hold you over until you're on your feet. Once you do, a backpack is necessary if you're going to carry more than the bare minimum of equipment. Backpacks are relatively cheap at the general store (don't get a knapsack -- they don't hold nearly enough), or you might hang about at the pawnshop and see if anyone has an old backpack they'd sell at a discount. If you see a backpack lying on the ground somewhere, do NOT pick it up, as it probably belongs to someone. If there is no one in the area, and the backpack is empty, then you're entitled to take it...if it's full, it belongs to someone and you should find someone with a gweth to announce its discovery. The last thing you want is to start your life with the reputation of being an item thief.
ARMOR --
Do not trot over to Tembeg's and pay for armour. Instead, go to the rock troll area (west of the first intersection in Kaerna Village, which is reached by heading in a northerly direction once you leave the Northeast gate of The Crossing), wait patiently outside the barricade (you can't climb over it until you're fifth circle, and with good reason) and politely ask anyone who comes along to snag you a nice leather cuirbouilli coat. The rock trolls drop them when they're killed, and most of the people advanced enough to fight rockies don't have any use for their armour.
Don't want to use leather armour? You'll have to pay if you wish to use something heavier. However, you can find shields in goblin territory.
WEAPONS --
If you wish to train in light-edged weapons, the easiest thing to do is pick up a short sword in goblin territory. For heavier melee weapons, try the pawnshop -- people are always upgrading, and if you're patient you'll eventually find someone selling an old weapon they've no use for. Since the weapons in The Crossing don't cost all that much to begin with, you can get a used one at an extremely reasonable price.
If you need a bow, try spending some time at the Ranger's Guild. Those industrious Ranger fellows churn out longbows like there's no tomorrow. Granted, they're not going to give away a well-made bow, but you can usually get an adequate bow for free -- people who are just learning how to make things love giving them away, since they know they're not good enough to sell them yet. I should know; I've given away any number of virtually worthless lockpicks.
OTHER -- Carving knives -- useful for skinning critters and whittling. You can buy these in the general store, but they're commonly found in chests dropped by goblins, so check the goblin area. You might also ask people that you come into contact with if they've an extra carving knife to spare; but be sure you ask politely, and NEVER yell.
Miscellaneous -- this is just a reminder to hang about the pawnshop if you're in a shopping mood. The pawnbroker, Cormyn, buys items at well less than half their value, so you can get a splendid deal on a variety of items by letting everyone in the pawshop know that you'll pay slightly higher than Cormyn's price for items you want.