Showers need to be cleaned no matter what surface you have. Just a fact of life, with minerals in the water, soap scum and other oddities.
Having said that, I don't see much of a difference cleaning tile vs. solid surface. I have both in my house and they have their nuances. Solid surface has no grout lines, but it does have caulk joints where the panels meet. Mildew builds up in the joints and you need to scrape out the old caulk and make it new again about every 18 months or so.
Ceramic tile has grout joints which, over time, will be where the gunk builds up.
As far as a door or a curtain, you need one. Unless you are talking about a truly walk in, doorless shower. Those require a fair amount of square footage to do right. Not sure how you're going to avoid cleaning the door, no matter what kind you have. Frameless doors have fewer nooks and crannies, but it's a shower, and stuff builds up. Curtains get scummy in a few months and need to be replaced.
If you're looking for a shower that doesn't have to be cleaned, you may be looking for something that doesn't exist. If you have the floor area (square footage) available to do a walk in, doorless shower, that is probably what you are looking for. Not cheap though. You need more tile for a walk-in than, for example, a 60" niche or neo-angle shower. And the tile needs to be installed, after a considerable amount of plumbing, framing and cement board work is done.
I just remodeled my master bath in the range of $10k-$20k, and I did all the work myself. The shower was custom glass neo-angle. I would think for a large doorless shower, you would be looking above $20k for the whole bath remodel, if someone else does the work. Probably just under $20k if you are doing the work.