I’ve just gone the opposite route – after many years finally moving of vinyl and cds to “digital”, and would second the above comments that a controller is basically the way to go, but with one more idea for you:
I’d say forget the CDJs completely – basically they’re not going to teach you anything more than using a reasonable controller will, nor be any more fun, especially when trying to be budget concious. At the very top end, being able to use the CDJs as a controller is quite a major feature, but even then they only work as fairly limited controllers, but will do severe wallet damage anyway – I’ve just bought a top-end controller with a bunch of extra toys for much less than ONE of the CDJs I would have otherwise bought, never mind the mixer I would have wanted to match them with.
You seem to be wanting to get more physical in your mixing, so what I’d maybe think might be good for you is to aim for a DVS-ready or upgradeable controller, and when you have the budget, hunt down some used 1200’s and try out timecode instead. A pair of used turntables will probably run you less a single entry-level CDJ too.
I haven’t got rid of the laptop for you, but I’m not sure why you really want to – once you have a controller, its less “laptop djing” than having a clear screen and a way to carry heaps of music without worrying about needing to burn CDs, skippping CDs, or finding *that* track that’s somewhere on one of these 10 discs… if you were thinking of USB sticks/SD cards instead, speaking from experience its still fiddly. And back to the thing about the screen, even the best CDJs are just poor imitations of the nice one you’ve already got.