How heavy should I lift for strength?

I am rather petite, don't really have extra body fat (I'm around 108lbs, give or take), and I would like to seriously begin to lift weights... my goal is to be strong; not "toned," and not "bodybuilder"... I am aiming for actual strength itself.

Other than my lifelong target of being healthy, I am considering the military, and am setting out to aim for the mens' physical fitness requirements (including acing the elusive pullups), as I don't believe in the modified requirements for women (it truly should all be equal).

I am looking into gyms and CrossFit... but my largest desire is to acquire the strength in a realistic, natural way that will actually assist me. Bodyweight and calisthenic exercises are of interest, among other things.

I currently own barbells, and am looking into dumbbells... but, to be honest, I am unsure of the weight I should be lifting. I understand, for strength, it is best to lift heavy with low reps... however, do you have any suggestions?

Adjustable dumbbells, in my opinion, wouldn't be ideal-- but I cannot have 20 sets lying around my house, at the moment. The adjustable ones range from 5 to 52lbs, and then another from 10 to 90lbs.

Would that be adequate? Should I look into something else entirely?

Thank you for reading, and I appreciate any insight, knowledge, and advice you offer.
How heavy should I lift for strength?
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