I have watched my screen be replaced on a few occasions, and it doesn’t seem terribly hard to do. Like, a little more complex than adding a video card to your computer, mainly because of the number of small parts involved.
But unless you are really motivated to do it, there are kiosks and cell phone repair places everywhere now. You would probably spend about $100, maybe a little less. A replacement screen that you install yourself is about $50. Personally, I think spending another $40-50 to not have to hassle with tiny screws and whatnot. YMMV.
It’s doable, but not easy. There are really tiny screws that are easy to lose forever, and flimsy cables that can be damaged. Getting the thing open easily requires a specialized tool that you won’t have. You can do it with a suction cup and judicious use of force, but if you pull really hard and it suddenly comes free, you risk damaging stuff as it comes open.
Go slow.
If you want to try it yourself, I recommend iFixit for parts (Link is to the iPhone SE screen + tools). They have well-written guides with pictures. (Disclaimer: a friend of mine works for the company)
It will probably take you an hour, or a professional 20 minutes. You should be able to get it done for under $100, with a 30-90 day warranty on the repair. Your call if your time/confidence in your steady hands is worth that.
It’s doable, but you’d probably be better off taking it to just a more generic repair shop for phones and such. My sister got hers repaired for like $60 or so.