The typical thing is a rock for engagement ring (which should be returned if the engagement is called off), and simple band for the wedding ring.
Rings need to be sized and since I am not a fan of surprises when entering property contracts that are legally binding, both parties should be present at sizing/fitting. This goes for both engagement and wedding ring. Buying rings then having to get them sized later is a hassle and generally not free.
I am also of the belief that both parties pay for their own wedding rings. Male fingers are generally larger than female fingers, so you're going to pay more for the wedding band, so a simple design can save you some $ by paying for materials.
Design and cost is up to you and yours. Don't be stupid about it or follow any out dated marketing ploy. More $$$ doesn't mean anyone one will be better off having spent it on what is both jewelry and symbol...and if it does make a big difference, you are barking up the wrong tree. Try not to impress others with rings that no one else cares about. Maybe spend a huge fortune if you need to have portable wealth for backup plan to flee the country, just know, rocks have crap for resale value. In Saudi Arabia, gold jewelry is mostly tied to spot price of gold, not design.
You can by-pass store front overhead by going with local "artisans". A friend at work had a wife who worked for PG&E and she did some ring making as a hobby on the side. I think she charged 10% over cost of materials. She'd melt the gold alloy in a little kiln at home, pour it, finish/polish and, well, I don't know how fancy it was, but, I don't know, it seemed like a nice way to do things. Maybe someone in the extended circle of family/friends you know does something like this or knows someone who does? Am sure there is a local arts and craft college or course that could be bent to your needs. (Example: for our wedding invite, Sweetie-pie and I went to local art store, shopped some paper, then talked to bored staff and asked if she knew of someone who could put together an invite and in short order got graduate student to do the rest on the paper and envelope we wanted.)