Sounds like you are just replacing components, so choice of guitar is entirely up to you. As mentioned, if you have a plan, it will go better for you, since you'll be able to pick a guitar that matches the objective somewhat.

In the most general sense, I would suggest any guitar with a full pick guard. That way you can do a "swimming pool" route, and experiment with all combinations and placement of pickups and electronics.

The greatest expense will then be new pick guard material (should get 2 from a $13 3-ply sheet). You can build any style of guitar, then change your mind and "build" another by making a new pick guard.

In more specific approach, go for a body wood traditionally used in the objective guitar. ie: mahogany for your LP style (maple cap if desired), and alder for your Strat style.