Beams is awesome but you are at the 4age level with your experience and budget. Keep the Beams goal for another day.
Budget is pretty thin IMO, you will spend twice that to install and maintain a 4age engine. Especially if you aren't a guy with a welder and fabrication skills yet.
16v 4age are all old now, you'd be hard pressed to find one that didn't need work to freshen up, and you could even say the same about 20 valves now, with the last ones being made well over a decade ago.
Beams would be ten grand when done, easily. There are gearbox length issues to overcome, tunnel sizing, mounts, fuel system. Brakes unless you want to die. Easy 10k DIY, or 25k at a shop.
SO the 4age, if you can find a motor and box for cheap, Id try to use carbs on it. Fuck efi, just use an ecu for timing and disconnect the rest. A simple Weber or some solex carbs and tune it. No need for fuel system, sell off the efi bits for the 4age that people want and then you can probably hit your budget. You can use the standard ae71 mounts and crossmember and pedals.
600 - ae71 parts
1500 motor and box
1000 carby and jets
800 - Exhaust, Radiator, hoses, fans, wires, clips and miscellaneous bits and pieces.
500 Programmable ignition
Bit over your budget but you would get to sell a few bits off the rwd 4age like the inlet manifold -$220, the Map sensor - $40, the injectors - $40, the engine wiring loom - $200 if you were going use carbs and not efi.
The beauty of the carb system is that you dont have to rip out the tank and fit an afi fuel system, which is one of the most un enjoyable bits and a costly exercise.