Hi - great question. How many copies are you looking to print? It might sound tacky but for less than 10-25, or so, often the digital printing in your own town is the best first place to look.
If you’re wanting other options, screenprinting two colors (usually black plus a highlight) is also better as a local choice, and you can usually get a really involved and interested press person to help you pick the best paper stock and ink. A typical yield is around 50-100 copies. It can be expensive as you’ll need to pay for camera work on the art, press time, etc. But you’ll be very pleased with the result. Screenprinting is awesome.
If you want to go exclusively online, then the options get very varied. If you’re looking to make 500-1000 copies of something then you have the option of offset printing. Offset is the best kind of printing for mass production but requires some understanding on your part about how inks physically, as a substance, add to one another in terms of density - the most common mistake with offset printing is a print that’s too dark because the designer (you) is calibrating the image off your screen and doesn’t anticipate how much darker shaded details become in a four-color process. This is less of an issue with lineart and flat color but still a learning process. It’s cool to learn about, though, of course.
Digital printing can subsequently be more forgiving, and there’s a LOT of print-on-demand options for you. But few of them would out-compete your local digital printer. Seeing what’s around (Kinkos/FedEx offers large format printing up to 11x17 and then larger with a plotter) - The only thing to watch out for with plotter prints is they can fade over time, so check about what inks they use and what paper when asking. Usually glossy holds up much better over time. With a plotter you can make gigantic prints.
I like Blurb a lot for single copy on-demand prints of books, but can’t speak for posters or prints. http://www.blurb.com - they work as a middle-person inbetwen Ingram Spark, but allow you to make a single copy of something, whereas Ingram asks for a $50 set-up.
I’d avoid ideas about drop-shipping before you know who you’re using. The term applies to sending out copies to your customers directly from the printing plant. It can sometimes be a really lousy mailer that a customer receives (or even mailed to wrong address) and if you’re wanting to make a small edition it can be better to mail yourself.
TLDR: How many copies do you want to make and what size?