I also started with a Lee Anniversary Single Stage Kit. They've updated it to be a bushing press now, it wasn't a bushing when I bought mine ~15-16yrs ago.

Eventually I bought a progressive press, then sold it, bought a different progressive press, sold that. Now I'm back to using basically that same Anniversary kit, but have added a Lee Turret Press. I use the original Single Stage Challenge press as a universal decapper.

I'd highly recommend that kit, then potentially add another $100 for a turret press to speed things up a bit for you.

What comes in the kit:

• Single Stage Press
• One Breech Lock Bushing
• Hand Primer for large and small primers
• Case holder set for hand primer
• Powder Measure
• Safety Powder Scale (it's actually a balance, not a scale)
• Powder Funnel
• Case trimmer and lock stud
• Chamfer tool
• Primer pocket cleaner
• Case lube

I'm sure I'm forgetting a few things that I use, and every reloader will have their own personal preferences for gear, but here's what I'd recommend, above and beyond the kit...

What DOESN'T come in the kit that you'll NEED (minimum):

• Quiet, clutter free, well-lit space to work (no TV in this room)
• Bench to mount it on/work on (Black & Decker Workmate with a 2'x2'x3/4" plywood bolted top is a fine "space saving" and "budget friendly" option)
• Reloading Manual(s) (best to get a few, get info from your powder manufacturer AND bullet manufacturer both)
• Components: Brass, primers, powder, bullets
• Dies for your cartridge(s)
• More bushings if you want to save time swapping dies
• Lee cartridge length gauges (I'd recommend getting an RCBS Pro-trimmer instead)
• Reloading blocks (holds cases while you're working)
• Case cleaner (ultrasonic or tumbler)
• Calipers (digital is worth the price)
• Ammo boxes (to store loaded rounds - can use factory ammo boxes, but be careful)
• Case cleaning and lubricating brushes
• Tubs to store dirty, clean, and trimmed brass (I use rubbermaid tubs)
• Lots of sticky labels (label your reloading blocks "sized", "primed", Charged", "seated", "crimped", label your ammo boxes, label your case tubs, etc)

What doesn't come in the kit you might want, even as a beginner:

• Turret press to replace the single stage
• Universal decapping die (use the single stage as a dedicated decapper)
• Powder Trickler (mega handy, sucks trying to spoon 0.1grn)
• Electronic case prep station
• Electronic powder scale or dispenser (double check on Safety Scale)
• Chronograph

The Lee Turret Deluxe kit is another good option, but you may be overwhelmed with the autoprime and auto powder dispenser at first. You also may not trust the auto powder dispenser for precision loading. Personally, I don't. I used to use a Lee Perfect Powder Measure (in the Anniversary kit) to feed onto a digital scale, trim with a powder trickler, then checked every load on the Lee Safety scale (actually a BALANCE) for precision. Now I have a Hornady electronic powder dispenser/scale, so I use that to dispense and weigh, then I check it on the balance before charging the case.

Like I said before, different strokes for different folks, but this is what I'd recommend for a beginner on a budget.