While view/technical cameras with digital backs do exist, you don't put them together in the same sentence with "affordable", as most are medium to large format. Most of the bodies start around US$6k (at least from what I'm seeing on B&H) and those don't include the digital back (sensor). Think in terms of five figure pricetags.
I would also say that a view/technical camera is several degrees above "serious", and using one is something of a lost art these days and probably done as much (or more) with film than digital, given the prohibitive costs of the gear.
Your best bet might be to get a regular digital interchangeable-lens body, and then a bellows adapter or tilt-shift lens, but this will only allow for lens movements, and with a TS lens, you won't have nearly the same degree of freedom for those movements as you would with a view camera/bellows.
I'll also add that movements with a TS lens--tilt in particular--were probably the most difficult thing I ever tried to master with my Canon dSLRs. It is not a simple easily-acquired skill to shoot with one, but does require a fair amount of practice.
And if all you really want to accomplish is the miniature effect, post-processing with depth masks or specialized software might get you there more easily with a lot less equipment outlay.