Since you intend to self-publish, you will need to spend a lot of time doing the non-creative tasks, such as marketing. A cover image is part of marketing. It is, in fact, one of the most important elements. It's the first thing that the customers see and they'll judge whether they want your book or not by it. If that cover doesn't attract and/or meet their expectations, then they'll disregard your book without hearing or seeing a single word about it. The cover illustrations are important for your book, so treat it like an important task. The wrong artist for your book can make it much more difficult for the right audience to find you. A particularly skilled artist can significantly boost your sales.
You can make this task easier on yourself by doing your research. Research the sort of covers used in your genre and determine the essential qualities that you'll carry or break in yours. Then, find some estimates for book illustrations. Determine what you can budget towards an artist. This will determine where you search. A low budget means you may have to hire a more inexperienced artist (from places like Deviantart or Behance). 396
A higher budget means you can save yourself some time and find artist representatives.
Art agencies are the closest thing to a 'quality check' you'll likely find in illustration. By going through an art agency, you will find an already curated list of artists that fit within that agency's niche. Those artists are a known quantity to their agents. The agents will have an idea of which artist can do what in what timeline and how much money they'll need to do it. They'll also be able to give you an idea of which of their artists would work best with your project because they, like art directors, work with many artists and/or businesses and have honed their eyes to what does and doesn't work. If any problems arise then the artists' agent will mediate. Even if the agent cannot help you, they might direct you towards an artist or a place that can.
If you don't have a budget that allows for that, however, then you'll just need to buckle down and look through portfolios. Do a couple at a time while you're eating or taking a break from writing. Looking at images is a quick process, especially if you did your research and predetermined what you need out of your book covers. You should know if an artist is right or not after looking at about 2-3 of their images. When you find a couple that you like (perhaps five or less), contact them.
Since you looked at those artists' portfolios, you shouldn't need any additional samples -- at least, none that require the artist to do unpaid work for you. To get the most out of your interaction with an illustrator, be thorough. Tell them your intentions with the images, how much money you budgeted for this project, what images of theirs you particularly liked and when you'll need those images. If your budget is not quite enough for what you're asking for, they'll at least have an opportunity to make creative suggestions that fit within your budget.
Good luck! 396