A simple but effective character is a Half-Ogre with good Melee and Dodge skills. He is easy to play and can hold his own in most combat situations.
Putting a point into Gambling at the start of the game will allow you to gamble with the first shopkeeper (and get more items than you would normally be able to afford!)
Be wary of armor sizes. For example, smaller characters like dwarves cannot wear normal or large-sized armors.
If you're already boosting certain stats to buy spells or tech schematics, consider buying skills that also uses the same character stats. for example, a mage might also look into buying Haggle since that skill is dependant on Willpower, or a technologist might buy Gambling or Heal since their Intelligence needs to be high
Find combinations of spells or skills that will work well together; don't buy something just because it "sounds" cool
If you're a magic user, be sure to put points into constitution as well. It helps to have extra Fatigue.
You don't have to talk to everyone in town, but if you do, you're likely to get more quests, which means more experience points.
Save often as you'll never know what lies beyond the next corner.
Use the arrow keys on your keyboard to scroll the isometric view while you use your mouse to move your character.
If you know many spells or have many items you want to put in your hot key bank, select the ones that need to be quickly accessible, not necessarily the ones which are often used.
Just because you got a fate point doesn't mean you have to use it right away. It makes more sense to use a fate point to help you do something your character has never been able to do before (for example, a fighter may save a fate point to successfully pick someone's pocket)
Being encumbered is no fun. If you must carry around bunches of heavy stuff, choose how you want the weight to be distributed. Decide who in your party needs to be the fastest.
Most puzzles in Arcanum have more than one possible solution. Experiment.
Find a good balance of skills to help you in town and in dungeons. For example, Pick Pocket might be an incredibly useful skill in civilized areas, but it won't help you at all when a horde of angry zombies are after you.
Dwarves have innate technological aptitude. Dwarves, therefore, make great technologists.
If you're going to be an explosives expert, make sure to put points in throwing. Your weapons are useless, otherwise.
If you're going to be a gunsmithy expert, make sure to put points in your firearms skill. Your weapons are useless, otherwise.
Remember, half-ogres cannot use guns because their hands are too big!
If playing as a firearms or bow character, consider carrying around a back-up weapon in the event you run out of ammo/arrows.
There are useful tech manuals out there that you can read to improve your Technological Expertise. Look for them!