I believe the "extra" ability to import a graphic is going to put anything way over your budget. Most lower cost machines don't come with designing software, and most have a pretty small display too. I bought stand alone software to do that and it was around $2,000. I bought it two years ago and have only used it once to divide up a grouped design. I really want to learn more, but time is limited. So for now I'm still buying designs. The software I bought pretty much does have the capability of creating a stitch file from a graphic. you can then go in and tweak it (like change fill patterns or or size). You tell it the size and what type of fabric you are stitching on, and it goes from there. It also comes with free upgrades.
I also bought software that you can draw out a design and it will create a stitch pattern. This is really neat if you like to do pencil drawing and want to create a stitch design. This needs a tablet that you can draw on to work, and the software lets you impose a picture that you can then trace over to create the stitching.
There is a lot involved and taking a graphic and converting it to a design that can be stitched out (it's called digitizing). There are also a lot of people out there that will do it for you at a modest cost, and a huge, huge number of already created designs you can buy for under $5. So to start out, just look for a decent machine and buy designs, and if you get seriously hooked, then you can deal with the rest.