If tinkering with things is you're thing, then give it a go. If nothing else you have a new hobby...
Lots of good advice already, but I'd pass on the idea of doing major stuff to a short scale Bronco/Mustang type bass, there's little in the way of parts to suit them and as they're a bit in trend right now they can run out to be quite expensive.
P and J bass parts, bodies and necks abound, so there's endless options and price ranges available. Plus those tried and proven shapes and layouts guarantee a balanced reasonably ergonomic instrument, with a range of tones that tick the boxes for what years of hearing them have taught us to recognize as "the sound of a bass guitar".
If you're happy with the wood grain showing, perhaps a simple wipe on poly or oil finish might be the go first time out. If you want a glossy paint finish, maybe buy a finished body, the Eden 'Premier' ones on ebay are quite good quality three piece alder under the paint and of course there's usually a few Squier's about. If you're looking to paint a raw body, perhaps consider alder, or poplar as body woods, they require little or no gain filling to get a smooth surface to paint over. Nothing ruins an attempted smooth glossy paint finish like deep wood gain pores showing though all over and filling woods such as ash to perfectly smooth is a pita if you aren't used to it. (Even if you are it's still a pita!)
I think you're idea of using EMG pickups is solid if you have no soldering skills and the price of their pickups is on par with Seymour Duncan, etc. when you consider you get good pots, wires, jack and all included. A parts P bass with a EMG passive pickup like their Geezer,(I quite like their alnico II evasive P as well, but tastes vary....) will give you a professional sounding instrument.
Maybe consider a decent quality bridge, over the cheapest on ebay? Gotoh stuff is excellent for not much more money that no name stuff same applies to their tuners/machine heads. Splash out a few extra dollars on a decent nut, if the neck you find doesn't come with one. I've always been partial to the graphite type synthetics over just cheap plastic.
Good luck and keep asking questions.
