I'm someone who has and still commissions artists several times for my personal projects, here are some tips. This is mainly for the standard digital png drawings.
1. If you're having trouble finding an artist, a great thing you can do is to go to communities/subreddits of games that are highly susceptible to anime fan art, such as Touhou, DDLC, etc, sort by the OC filter and find any OC art to your tastes, then get in touch with the artist, 90% of the time they will be open for commissions. This is great because you'll also be helping out lesser known artists as the same time.
2.Do a background check on the artist, mainly check their twitter, do they seem like drama magnets and/or are heavily political or is all they do on twitter is retweet other anime art? I find working with artists who do the latter are very easy and pleasant to work with
3. Get a contract, especially for big commissions, contracts help both you and the artist by preventing misunderstandings and making sure you're both on the exact same page with what to expect. You CAN use those template contracts you can find for free, but for something 100% rock solid you'll want to get a lawyer to make one if it's a huge, expensive commission. I personally use a 1 page template contract because that's good enough for what i need, but in one case I paid a lawyer to make one because I needed something absolutely solid as it was a huge project.
The cool/sad thing about art commissions is that it's a buyers market, unless you're looking for something extremely specific, there are tons of artists to chose from who will be more then happy to help you out, you just have to put effort into finding them.
