Yep freeweights, get your diet right and maybe use a protein powder to top up your protein intake (you need to be taking in 1-1.5g of protein per kg of bodyweight.)
Though you will be limited to upper body as you will struggle to do you legs properly with out a squat rack and lots of plates.
But from your post that doesn’t appear to be the issue.
Also, not convinced that heavy weights on legs is compatible with regular cycling anyway. If you train your legs properly your legs will be sore for a week afterwards.
The split I use for upper body:
Push
Dunbell Bench Press
Shoulder Press
Dumbell Flyes
Close Grip Bench
French Press
Pull
Dumbell Rows
Shrugs
Reverse Grip Curls
Preacher Curls