I'm not a pro at 3D printing or painting, but I think I know enough to answer your questions.

Ok, so first thing out of the way- that model you linked is not made for 3D printing. To get a decent result you're gonna have to edit it a bit.

This is intended to be a hand-held prop, not just a display model. So my first question is, is that even feasible? I don’t know how strong things like this are. I’m not going to be hitting anything with it, but a little bit of waving around I think would be in order.

Definitely feasible. There's a wide range of durability with 3D printed stuff, but you'd have to go out of your way to make something that can't handle that.

Assuming that’s ok, what material should I use? Not entirely sure I even get a choice but I think so?

PLA is the default, and it would work ok, you could also switch to PETG. PLA softens at a very low temperature- roughly 60°C. It's not too big of a concern, but there's a small chance of it deforming if, for example, you left it in a very hot car, or under a window that happens to focus the sunlight on it. For a prop like that you don't have to get more fancy than that. You almost certainly get to choose- I don't use these 3D printing services but I'd actually be slightly concerned if they didn't.

Another question I have is about painting. I’ve seen painting guides online, but one question I have I didn’t find an answer to is again, about it being hand-held. I don’t want to use a paint that will come off or smudge with sweaty palms. Are any kinds better for that than others? Are any?

Even just regular craft-store acrylic should hold up decently well, but you should use a sealant/clearcoat/varnish. I don't do this so I can't help you much with that, but it should be as simple as just spraying the whole thing with it after you're done painting.

And how close could I likely make it look like in the link? It doesn’t have to be exact, but there’s metallic parts, glassy parts, kinda gives a glowy impression… or is this going to be too hard for someone with no experience? (I’ve painted a couple of model kits when I was a kid.)

Probably not very close. The metallic parts are ok, there's paints that mimic metal, they're not going to look fully convincing but it'll probably be fine. You can get glossy clearcoats too. The big issue is the glowing part. There are ways to make something look like it's glowing by using gradients and stuff (look up OSL painting) but I don't think that works very well at such a large scale, and it's difficult. For something this big I think the only way to get a good effect is to make it actually glow, which is a whole 'nother can of worms. To make that part look good, you're going to have to do a ton of work. I haven't done anything like this before, but I've got some ideas for how it could be done.

Do you want to make a lightsaber, or specifically this lightsaber? If you aren't particularly attached to this one I'd suggest looking for another model. Printables, Thingiverse, and Thangs have 3D models specifically designed for printing.

There is no issue to print this. But...

If it's handed, it's quite big. It has to be printed into multiple parts. I would make the metal things and the glowing thing separately.

The glowing thing will look like shit if 3D printed. You better should get an acrylic rod. You need a bunch of blue leds too.

There are filaments that look metallic. Or you would get better results by sanding it and painting it with special paints.

The whole project could be expensive. (~100 to $150)

Without edditing the model, they can split it in 2 parts (or more) in slicer software (which is used anyway). That way you need to glue them together, sand and paint. How it looks will more depend on your sanding and painting skills than 3D printing quality. Printers can usually print up to 200 or 300 mm in all 3 dimmensions so you will end up with that many parts depending on how big you want your final product to be. Probably best to choose PETG or ABS filament since they are common and will not melt on the sun. Best to convert the file in STL and ask for a price. This kind of model, if split in 2 halves, shouldnt be difficult to print even without supports

I can’t answer everything because I don’t make models myself, but don’t buy a 3D printer. Getting it set up and calibrated takes ages, as well as the learning curve. Find a service online, you send them your file and they print it and send it back. PLA is the most common material for printing and I expect it would be fine here, I haven’t really used anything else and I have no problems. You can just make the plastic thicker to make it stronger.

The painting part should be fine but you’ll probably have to use a primer. Get a few prints so you can make mistakes.

Just find an online printing service and they should be able to answer a lot of your questions.