Go with OEM wheels, and you'll be fine. 5x100 bolt circle. 15, 16, or 17 inch. I'd recommend 16 inch, as you'll get a little better handling available, and the tire prices are a little easier on the wallet as opposed to 17s. 18 inch wheels are probably available, but they're just silly as in expensive, and the guy mounting them won't like you very much. That's because it is significantly more difficult to mount low profile tires, and the 18" size are 40 percent in aspect ratio. If you stick with OEM, you won't have to buy new lug bolts.
This is assuming you currently have OEM wheels.
Is that what you're asking? Any other details you'd like to provide? The wheels list at the beginning of this thread show the available wheels, but some of them are very hard to find. Having said that, those available from private sellers probably won't be perfect, but they're a LOT more affordable than new retail. And if you just look locally, you'll find the shipping a lot more reasonable since you just go get them.
Yep - stick with OEM rims. Aftermarket - you deal with adapter rings (which often don't fit perfectly, and you have to buy new bolts - around $4-5 each, so $100 after tax for a 20-pack, plus probably deal with the stupid lug bolt "key" that lots of aftermarket bolts use.
For the 2003 Beetle, as Power Hound says, 16" is the sweet spot: lots of tire options, good price, handle nicely. A good do-everything, year round tire (even for winter) is the Continental DWS 06 (Dry, Wet, Snow).
Check out Kijiji or Facebook Marketplace near you - there's always people looking to get rid of rims / tires. Just be sure they're 5x100 (ask or look for part number; if it starts with 1J* or 1C*, you're good; if the second letter is a K - like 1K0 *** ***, that's a 5x112.