I have a Therma Tru fiber glass door that has worked out very well. I staineed it myself and it was easy, nothing to it, so consider doing that part of it yourself.

Abbey

I have a Pella wood-grained fiberglass entry door with sidelight. I also bought mine at Lowe's. It was $2k cheaper at Lowes than it was at the Pella store. Exact same door.
I paid Lowes for the installation, and finished the door myself. I don't remember the intallation cost, but it wasn't more than a couple of hundred dollars. It was an exact match size wise to the existing hole. Regarding staining...I used a Bartley gel stain and followed Bartley's instructions. Because the stain doesn't absorb into the wood (fiberglass) you have to wait for it to dry on the surface. I applied two coats of stain and two coats of poly...took about 4 days per side. I don't think you'll find many fiberglass doors that come stained. Too many variables. It's easier to custom blend a stain that matches your existing woodwork than buy a prefinished door.

I've seem them come stained, I know the Feather River Doors from HD can come stained, and I would guess, there are other door companies that can come stained.

My parents have a Pella fiberglass entry door. They like it, but it was pricy. They painted theirs and had it installed

Feather River door worked out great for me. stained and installed it myself and i am very happy with the product and results. instructions for finishing and hanging were very clear and straightforward for a beginner to be able to do this task.