The Only Tools You Actually Need
Start with a loupe — a small folding magnifier. Get a 10x loupe with a glass lens; decent ones cost $10-$20. This is the tool you'll use constantly for checking mint marks, doubling, and wear. A 5x is fine for general looking, but 10x is the standard for variety hunting. You don't need 30x or 60x; past 10x-16x the field of view gets so small it's actually harder to use.
Second, a digital scale that reads to 0.01 grams, about $15-$25 online. Weight is the great lie detector in coin collecting: it exposes fake silver, plated novelty coins, and confirms real errors like wrong planchets and missing clad layers. A cheap jewelry scale is fine.
Third, optionally, digital calipers ($10-$20) for measuring diameter, useful for broadstrikes and suspected wrong planchets. Add a soft towel or pad to work over, some 2x2 flips for keepers, and good light — a cheap desk lamp you can angle beats an expensive one overhead. That's the whole kit: under $60 total. Skip the fancy microscopes until you know you need one.