So as far as I understand I can raise both Strength and the skills affected by it like Combat and such separately? What's the purpose of this? Should I just be looking to see what spends the least ability points?

Yes, Strength and the skills affected by it can be raised separately.

Raising your Strength will by proxy raise all of the skills it affects, while raising an individual skill only raises that skill. Generally speaking, raising your basic stats (like Strength) is going to be significantly more expensive than raising any given individual skill because the basic stats affect multiple skills.

You'll need to balance how many AP you are willing to spend in order to achieve certain levels of skills. For example, if you really just want lots of Combat, then spending directly on Combat is more efficient than spending on Strength. If you want to raise Combat, Health, HP Regen, and Damage, then spending on Strength may be a more efficient use of your AP instead of trying to raise each skill separately.