See what the manager/owner in the place wears day to day, and dress a notch or two above that. Not enough to overdress, just enough to say "I am aware of the standard you have set and am endeavoring to put my best foot forward because I take this seriously."
If they're wearing denim and polos, replace the denim with slacks, and replace the polo with a button down. If they're wearing slacks and a polo, make it a button down with a tie. Or nicer dress pants and no tie.
Polish your shoes. If you don't own polishable shoes, buy some and wear them.
Based on what I've seen in different computer repair places, you'll probably end up wearing slacks, button down shirt, and probably a tie. Make sure everything is ironed and/or pressed.
You can usually get shirts cleaned, starched, and pressed for $2-$3 or so per shirt. Set up a rotation, use a bit of febreeze, and wear them a couple times between cleanings. (When I was dressing more formally for work, my cleaning bill was only $30-$40 a month. I did my own pants though.) Silk looks nice, but it's usually more expensive to clean.