In general, I buy most of my tools and supplies from RioGrande. Otto Frei and Contenti are great alternatives as well. Links I provide are just an example of what I use after trial and error but feel free to experiment.
General Bench Tools: a basic list of hand tools to get you started
Magnifying visor: to work under magnification. Optivisor with a couple of lens options works great for most of my work. Beware: Amazon sells similar LOOKING visors but they’re CRAP. Donegan is the original and their glass optics are great. Haven’t tried their acrylic lens option but they’re less expensive.
Pliers: after using lots of kinds of pliers for metalsmithing, I find these to be my go-to’s. I prefer parallel action to regular pliers when available because of less surface damage to pieces and they hold pieces securely in almost any situation with less pressure.
‣Round Flat nose - https://www.riogrande.com/product/flat-and-half-round-forming-pliers/111180
‣Needle Chain nose - https://www.riogrande.com/product/pliersswanstrom-needle-chain-noses230e/111303
‣Parallel Chain nose - https://www.riogrande.com/product/swanstrom-parallel-action-fine-flat-nose-pliers/111669
‣Parallel Flat nose - https://www.riogrande.com/product/swanstrom-parallel-action-flat-nose-pliers/111667
‣Bail Making pliers - (replaces round nose pliers) https://www.riogrande.com/product/bail-shaping-pliers/111957
Ring clamp, parallel: sooooo much better than a traditional ring clamp and very cheap. https://www.riogrande.com/product/parallel-jaw-ring-clamp/113969
Saw frame: many choices here and this is one of those tools you just have to feel to know which one you like. I have tried a traditional, wholly adjustable frame style and didn’t like it much, others love them. I’ve never needed the adjustability. I like Green Lion: https://www.greenlionstudios.com/jewelers-saw-frame, or PotterUSA (almost always out of stock).
Saw blades: get both 2/0 and 3/0 sizes to start. You will break many blades when you're learning so buy several dozen of each size. You can buy an assortment of sizes also, but buy extra 2/0 and 3/0. Don’t buy the cheapest ones, buy Hercules or Rio’s LaserGold, for example.
Hammers: there are two categories of hammers. Hammers for hitting other steel tools and hammers for hitting your precious metal work pieces, NOT to be confused! You'll need both kinds.
‣Chasing hammer for hitting tools, flat face - https://www.riogrande.com/product/fretz-revere-chasing-and-riveting-hammer-r-cr/112395
‣Non-marring dead blow hammer - https://www.riogrande.com/product/delrin-deadblow-hammer-cross-peen-and-flat/112472
‣Goldsmith/Cross Peen hammer for general purpose work piece hitting - https://www.riogrande.com/product/fretz-revere-goldsmith-and-cross-peen-hammer-r-gf/112396
Bench block: Steel, 4 x 4 inch is a good size to start. Get an old mouse pad to put under it to dampen the sound.
Bench pin: type depends on your work area, might be a good idea to get a clamp on to start. https://www.ottofrei.com/Combination-Bench-Pin-Anvil. Ultimately, I recommend a GRS system.
Sand paper: this stuff rocks! Can be used wet or dry and it lasts a long time, has more consistent grain size (better results). https://www.riogrande.com/product/3m-imperial-micro-finishing-film-assortment/337310
Scribe: any will do, they're cheap