Welcome to the forum! Looks like youve been doing some reading so far but I would make a few suggestions. First off you'll definately love a 5spd, whole different car. Since you will have to replace the ecu (i think you do right? havn't done it myself) I would suggest going to a stand alone after market ecu when you do the tranny swap. You will need engine management if you plan on making any type of power, you mentioned doubling the horsepower. Thats around 200 rwp. I don't know exact figures, that may be "possible" with bandaids but that would be the maximum you could ever make. Not to mention you would probabbly end up spending more on the bandaid setup than you would just going to a megasquirt setup. The megasquirt is very popular on this forum, it can be had for around $350 for the ms2, sensors and harness plugs and wiring but you have to do it all yourself. I myself went with a diypnp for my 00 miata, its $450 plus an IAT sensor ($20 I think?) but most of the stuff is setup already, just solder in the resistors using the instructions, if you can solder its about as hard as a lego kit. Also your harness will plug directly into the box, you don't have to build a harness. Here
is an instruction guide on how to make one for your exact car. Also with either one you will have to get a wideband 02 sensor, ussually around $150.
You will still have to modifiy the harness for the 5spd as you would before but shouldn't be that hard. As far as the turbo project goes just do alot of reading and decide if you want to buy a kit or put one together yourself. If you do the research it won't be too hard to purchase a used manifold/downpipe setup. Thats the most important part of the setup, after that turbos, injectors, intercooler setups, and the other stuff are pretty easy to come by to fit your needs, just make sure the turbo fits the manifold/dp. You'll just have to do the research, Begi and flyin miata make excellent kits though that take out the guess work. Also, when you do the transmission swap, save your self the headache and get a clutch that will hold up to your power goals. Its really not that much more for a decent clutch over an oe one.
To sum this up I would suggest upgrading in about this order:
4. Turbo setup (not at the same time as ecu/tranny though, get those up and running first)
This forum has a massive amount of information and the people here will help you with any question you could have... but nobody will spoon feed you anything. Search first, if you can't find it using the search box googling it usually works best. Just type in "site:miataturbo.net 5spd swap" or whatever it is your looking for. Good luck