Unfortunately for a high quality "mirror" type paint job, you'll have to either get the expensive stuff, or hire a pro to do it (and they'll be using the expensive stuff). If you just want it shiny and don't care too much about whether you can see yourself in it, you might be able to get away with a very, very careful application of high-shine spray can metallic. I'd suggest doing a test piece (or more as needed) to perfect your technique, as well as to test if gentle wet sanding (have to be very careful not to scratch or gouge the paint) with a high grit (ultra fine) sanding sponge, or perhaps a buffer and compound, will give the desired result. It's also best to lay down as bright of a primer/base layer as possible before you spray on the metalic. If you use a black or even a dark grey primer, you'll end up with a duller finish than if you used a lighter gray or white primer (or light grey primer and a base coat of white paint). You'll also want to avoid a top coat, as even a clear/gloss top coat can dull the metallic look. And when you're painting, remember that 3-4 light coats will end up looking a lot better and achieve the same coverage as 1-2 heavy coats. I've seen a lot of builds and projects here and elsewhere that quickly went from looking pro to looking like a middle school art project because they rushed the paint and ended up with drips, runs, overspray, feathering, and other blemishes that could easily have been avoided if they took their time. Investing in a roll of painter's tape and semi-heavy masking paper is also a great and overlooked idea, as regular masking tape can bleed through, and so can newpaper, although in a pinch a double or triple layer of newpaper can work well enough if you're not heavy-handed with the paint and be sure to let it dry between coats. Most spray cans will have directions on them that indicate how long to wait between coats, and how long to wait before it's dry enough to switch to another color or start handling the piece for normal use, although that time changes slightly depending on the temperature and humidity. Warmer and drier is best, obviously, and colder or damper means it's better to wait a bit longer than the recommended time.
Another tip if you will be using the tape to define the edges of the area you're painting, after the paint has dried fully peel up the corner edge of the tape opposite of where you were painting (to avoid marring the paint while digging up the edge of the tape) and pull the tape slowly and evenly back upon itself at a sharp angle. Don't pull it straight up, you'll want the tape to make at most a 45 degree angle. This will help cut a more crisp line through the paint that will have sprayed onto the tape while you worked. If you pull it straight up or just try to pull the tape off any which way, there's a chance of either leaving an uneven break on the tape side, letting the paint go beyond the intended line while not being properly adhered to the piece, making it easy for the paint to peel, or it will break into the painted area itself and start peeling away your paint. Another way to avoid this if you have a very gentle and steady hand is to uses an exacto or razor knife and very lightly trace along the painted edge of the tape. The risk here is that if your hand is not steady or you press too hard you could scratch up the paint or cut right into the piece you're working on, and that can be a real pain to fix.
Another tip if you will be using the tape to define the edges of the area you're painting, after the paint has dried fully peel up the corner edge of the tape opposite of where you were painting (to avoid marring the paint while digging up the edge of the tape) and pull the tape slowly and evenly back upon itself at a sharp angle. Don't pull it straight up, you'll want the tape to make at most a 45 degree angle. This will help cut a more crisp line through the paint that will have sprayed onto the tape while you worked. If you pull it straight up or just try to pull the tape off any which way, there's a chance of either leaving an uneven break on the tape side, letting the paint go beyond the intended line while not being properly adhered to the piece, making it easy for the paint to peel, or it will break into the painted area itself and start peeling away your paint. Another way to avoid this if you have a very gentle and steady hand is to uses an exacto or razor knife and very lightly trace along the painted edge of the tape. The risk here is that if your hand is not steady or you press too hard you could scratch up the paint or cut right into the piece you're working on, and that can be a real pain to fix.