What Is your best advice for anyone getting into making illustrated products?

Artist interview

I think ditching this term "product" is a good idea. Unless you become a graphic designer. If you end up as a gallery artist or illustrator do yourself the favor of calling your work art, and not a product. Otherwise people will treat you like a machine or a business person, and not respect you as a creative person with an artistic vision.
As far as utilitarian items with your art on them, I don't have a huge amount of experience with that. I made t shirts for a while and while its an easier sell than a piece of art, its a total pain in the a**. Keeping the right cuts in the right sizes in the right colors was always annoying. But t shirts work really well for some people. The thing to keep in mind is this, you don't want to undersell yourself. If you have a $100 silkscreen, and the same image on a $25 shirt, you will sell the shirt every time. If it's a stong piece, You'd do better to not offer the shirt and sell the 100$ prints. So try not to undersell myself, and putting art onto objects sometimes means you have to make it cheap, and then you're shooting yourself in the foot. People expect t shirts to be affordable, they think a tote bag shouldn't cost more than 25$, or a mug more than $25, whereas, art goes for whatever you ask for. Still, if you need to pay the rent, t shirts are a good way to go, i mean, its easy to sell affordable useful objects but that won't necessarily build up a fan base or a career.
Also I have to say if you're being hired by a big company, don't undersell yourself. Don't be afraid to throw some decent numbers around, first the more people have pay you, the more they will value your expertise and effort, and treat you as a respected peer. You open price talks in a negotiation frame of mind. It's better to throw a laughably high price out there and have them talk you down, than to start with a small number and have then snap it up right away and you realize you could have added a zero onto that, no problem, and you just screwed yourself. You will get a lot of pressure to provide cheap or free art to big companies to build your resume or "get exposure", but providing free art leads to more jobs that expect free art. And that can go on for years taking you nowhere. And the more artists allow themselves to be exploited, the more difficult it becomes for any artist to get paid an actual living wage for their work. This is a huge problem!

How do you go about pricing your work?

Silkscreen artist based in NA
(Prefered to be Anonymous)

I've changed how I price my work over time. When I was in college I priced according to what I could afford, which I think is not a bad way to go if you want to build up a fan base, but it doesn't do much to impress the gallery system or any other snobby art institutions who measure work by its monetary value.
Then as I got it older it changed into "what is my time worth? What are my skills and experience worth? what are people willing to pay for this?"

Can you predict what products or pieces will sell better than others? If so, how?

I think I can, but then some pieces will surprise me. What works best will be different for every artist but many of my customers like comforting familiar imagery, nostalgia, animals, cute stuff, old fashioned illustration type stuff. But I'd rather make weird stuff, so generally the weirder I go, the less success I have. But that's because my art style 15 years ago attracted that fan base. And as a street vendor I did cater to culturally illiterate regular folks who would go for a realistic cat over some trippy strange monster or something. Still sometimes a thing I assume no one will like will be really popular, and sometimes no one will like a print for the first 5 years after I made it, then suddenly it will sell out. So it isn't totally predictable. One sad but true generalisation is the average person will be drawn to realistic images, the more rendered and detailed the more it will seem like "good art" to regular people. And i don't recommend catering to any of this!

As a young illustrator should I focus on the quality of my products or making my work affordable to get it out there in the world?

Quality should always come first. Quality is what builds a fanbase, and a solid fanbase will keep you afloat. A slow build with quality art is what I recommend. Don't expect success right away, it takes time. It takes years to develop interesting work, and an interesting style, and it takes years to build up a dedicated following, or solid relationships with art directors and editors. But overtime quality will lead to more long term success.