Welcome to the forums.
First off I would give the forum rules a read just to get familiar, runs awesome is great, but it is not easy to get facts off of. Some numbers like good compression values would iterate the point more clearly in a factual manner that would make it easier to convince others that your engine is indeed awesomely running.
The reality is that an L28ET swap will be easier, cheaper, and more powerful in the end, but I don't mind bench racing once in a while. Is there a reason that you don't want to swap in an L28ET? Or is there a reason why you want to keep the L24? If it is just plain old boneitis then your fishing for having your cake and eating it too which is pretty daft.
First off we need a baseline, what do you have? What head and what block? What resources? What skill? What aptitude?
I am not sure what the exhaust ports have to do with the fuel rail not fitting. The L24 head INTAKE port probably doesn't have the injector reliefs to take the factory injectors.
If it is an E31 head the square ports will take an L28ET manifold from what I remember.
Your second category is glossing over a big thing, fuel is important, how do you plan on getting fuel to the motor, blow thru carb? Draw thru carb? FI connversion? Man with a spray bottle?
Spark management is also important, stand alone spark control? Aftermarket ECU? Fixed distributor? Man with a match?
High compression/flat pistons generally means you have to play with timing a bit more, run higher octane, and most likely you won't be able to run as large a PSI of booste. I want to say most of the combos keep this motor from being an interference motor so I don't think that is as big a concern.
You aren't really going to be finding any of these parts off the shelf, it is going to be on craigslist or ebay most likely, occasionally a junkyard or auto parts recycler.
Cheap and reliable don't go hand in hand here with the exception of the L28ET as that is fairly cheap and as it was an OEM offering so fairly reliable. The cheap way to do some things will just be a liability down the road, that doesn't mean you need gold plated exhaust studs or anything like that, but it does mean that gluing fittings onto the pan, running ebay parts, running bandaid setups will compromise reliability.
For example if you want cheap you would fix the distributor to one timing setting, but without the ability to control spark, you will be running the engine in un-ideal circumstances part of the time either on boost or off boost which leads to early wear if not outright failures. If you want cheap you would do a draw through turbo, but one hiccup on start up or backfire and you will be blowing out your intake as well as turbo and carb.
With that in mind your budget is pretty light.
For a basic conversion, keeping the L24...
Oil feed line
Oil return line
Oil feed fitting
Oil return fitting
Block oil feed fitting
Block oil return fitting
Fuel pressure regulator
Crank trigger wheel or dizzy
Intercooler piping joiners (silicone couplers)
A decent turbo is going to set you back about $600 off the shelf and the cheapest ECU that could run engine with some control will be a megasquirt and that would be about $400 (both those numbers are rounding down). That is half of your budget gone.
If you were going as cheap as possible you would be taking this stuff off of an L28ET, but once you take off all the parts you are going to be left with basically a stripped long block which wouldn't function anyways. Given how easy it is to pull the motor in our cars it would honestly be more effort to transfer everything over then it would be to transfer the block which is why people would recommend otherwise.
I would recommend you sit down and write out what you want and why.
Your overall budget is pretty decent, put a bit of money into the suspension and the interior and have a numbers matching driver would keep the most value and keep you entertained. I want to say Rome listened to forum advice and ended up with a pretty sweet turbocharged ride in that ball park.
Now if you were to say limited to that budget by some rule set like you had an actual guideline you had to follow, there are some interesting ways to boost an L24 on a dime and nickle budget, but without knowing your mechanical aptitude and skillset, I wouldn't be anywhere close to recommending you go down that road.