If you're looking for budget, you don't need a sump and related pump/plumbing. It's nice for the extra water volume, but it does add cost and complication.
If you don't want to go with a reef, then yeah... $500 is doable. If you keep your stock levels down, you can probably skip the protein skimmer so that will save you.
So for a sumpless budget 45g FOWLR
, using your existing tank and lighting, you're looking at...
Rock (45 lbs of "base" rock, 20 lbs of "mature" rock with critters)
200W Heater (or 2x 100W heaters)
2x Powerheads for circulation
Algae cleaner magnet or scraper
Ammonia/nitrite/nitrate/pH test kits
Bucket of salt
Something to store salt water in between water changes
Powerhead and heater for the saltwater storage
Use of tap water can lead to algae issues down the road, so either buying a RO
water filtration unit, or buying RO
water somewhere is a good idea. But if that's not in the budget, just remember to factor in a good dechlorinator.