The general rule for almost all spells/skills is that by upgrading you increase the output of the spell by a percentage and that percentage increase is greater than the increase in the power cost to cast it.
For example, you may have an APP4 Direct damage spell that costs 10 power and does 100 damage, the ADEPT1 version may do 115 damage and cost 11 power. ie for a 10% increase in power you get a 15% increase in damage.
Effectively your skills/spells get more "power" efficient as you upgrade them from APP1 to ADEPT3 and beyond. This holds true for almost every skill/spell.
This translates in game terms to quicker kills (and therefor lower health loss) and less power used to achieve the kill (and therefor less down time and vulnerability between kills).
Efficient use of power is possibly the most fundamental concern of soloists and group players alike, so you should always look to have APP4 in any skill at the first opportunity. In reality you will be restricted as to how far you can upgrade (Adept1 to 3) by your cash flow. Buy what you feel comfortable with. If a spell upgrade is going to cost you 10gp but you can improve your character more with an equipment upgrade that costs 1gp, upgrading the spell would obviously be an inefficient way to go.
You get the best bang per buck increase going from APP1 to APP4 (considering most APP4's are <40s). If you are flush with cash, go all the way to Adpet3 too, if not don't sweat it, your money is probably best spent elsewhere.
Also, examining spell/skill upgrades on the vendors will tell you the gains you will receive - by doing so you wont be flying blind when following the skill upgrade path.
*Spoddie*