I have a 73 240Z that originally had the L24, which I then turbocharged with a draw thru Stromberg carby (more power, but less refinement). Then I put in an injected turbo L28 with 400HP which went like a cut cat, but sounded and felt like the truck engine that it is. I now have a RB25DET at around 500HP, but probably less torque than the L28. THe RB25DET installation would have $15k of parts in it, and if you added the labor, closer to $30k. So why did I do all that? It wasn't for the power....in an 1,100kg road car, what can you do with 500HP that you can't do with 400?
In a word....REFINEMENT. An L series can make plenty of performance, but an RB is a million times smoother. It's not just the engine either...the (larger) transmission and prop shaft and Uni joints deal with the torque much better and you get nothing like the vibration under hard acceleration...the RB sounds better too, and with VVT gives comparably good bottom end torque for an engine that also loves to rev. So, if you want refinement, go the RB, but you will struggle to do it for that budget, even if you keep everything stock.
If I was doing it on a $5k budget, I'd just do the L series up to a warm config (perhaps go an L28), and put your effort into simple enhancements that won't cost much. I wouldn't worry about injection...twin carbs will make plenty of power, as will triples, but they cost money to buy and keep tuned.
One of the most fun 240Z's I ever drove just had a warmed over carbied L28 and it had stacks of power for road use and was easy to keep running well and very durable.
If you go the RB20 you will have less torque than the L28 due to both capacity and the flow characteristics of a 4 valve head....you'll take the car backwards for road use, although it may be more refined if you do it well.
RB conversions go best when a fair bit of money can be thrown at them...if not, you'll get a better overall result enhancing the L series.
Regarding some of your questions...I can assure you enhancing an L series is nowhere near as complicated as installing an RB in a Z. There is quite a bit to it if you want a nice result.....sure you can shoehorn it in and have all sorts of things not work or fit properly, but if you want to do justice to the potential of the base engine, you need to do the installation thoroughly and attend to all the little details that take time and tend to cost money, even if a few hundred bucks at a time.
Finally...what's all this appeal of fuel injection??? Back when I was 19 and first bought my 240, it started up just fine with the carbies and ran plenty hard. Injection came along to deal with emissions, not make more power. If you've got an old car that doesn't need to meet emissions, stay with the classic look of carbies and enjoy using the choke lever on cold mornings!!
Cheers
Jamo