How much detail is involved and the canvas size is how I generally base my pricing. Personally I require half up front, which will cover my time if someone backs out and also my materials which are really expensive since I use professional grade art supplies. Canvases made out of linen or premium oil paints like Old Holland are insanely expensive -- but ultimately worth it. For example, one 125ml tube of Old Holland Cadmium Red is $132.00!! It will disappear quickly as a primary color because it gets mixed constantly, but the difference in pigment load, consistency, texture, and longevity of that paint versus some Windsor & Newton student grade paint is night and day. No joking there are folks who think oil paint costs what house paint does at Lowe's. I have to explain that it protects the clients work -- you don't want your painting that puts a smile on your face every time you walk past it and paid hundreds\thousands of dollars for yellowing, cracking, or the color fading in 10 years because the artist used crappy materials. A lot of clients will see a beautiful finished piece and think you used all student grade garbage from your local Michael's and it's a constant education about the up front cost and time investment.
I have all but retired from privately commissioned art pieces anymore because that experience fucking sucks the life out of me. It's filled with overbearing clients who want to offer you 100-200$ for something that took days/weeks and on top if it most clients have no artistic vision and think they do.
Anyways, it really is imperative you see a portfolio of finished work and make sure it's what you want. Price is really subjective, and you will hear rules about how much to charge and pay which are all over the map and varies from artist to artist. I used to get incredibly anxious trying to justify price till I talked to an artist who sold his paintings for 5-10k a piece and asked him what he said when people bitched about cost. He laughed and said it was not his job to make it affordable any more than any it is in other profession to make a service or product affordable. Nobody is going to walk into a Ferrari dealership and bitch and complain about the cost of a Ferrari because they can only afford a Honda Accord. It changed my perspective forever. Someone doesn't want to pay me for my time for original artwork? They can fuck right off. Go buy a poster or a print from Bed Bath and Beyond. It's also given me the freedom from the guilt trip of owing a "friends and family discount" to those people in my life just so my uncle can give my aunt an original art piece for their anniversary from their favorite nephew. Pay up bitch.