I'd second the Prusa if you can stretch it. There's also the mini that Prusa released, but the backlog on those orders is quite literally months long at this point. If you can wait, and you can't stretch the budget to $750, I'd shoot for the mini.
One of the things to understand about most of 3d printing is that is it not yet a 'solved' problem in the way that say, normal paper printers are. There's a good deal of tinkering and tweaking that goes along with the hobby. I only mention this because you want to choose a printer that has a large user base (and therefore, support base). I'm not familiar with the anycubic, but the Ender 3 Pro has a large install base and I would be pretty comfortable with being able to access support for that printer.
To answer your question about software, you'll need both a design program and a 'slicer' that will turn your design into G-Code which the printer will execute to create the object. Prusa printers come with a custom slicer called PrusaSlicer. There's also several free options out there, such as Cura.
On the design side...well, thats a much tougher nut to crack. It really depends on how sophisticated you wanted to be. The high-end answer seems to be Fusion 360. You will have to dig around on the site to find the hobbiest lic. as they've buried it away behind scary looking 495$/yr subscription models, but you can find it. At the other end of the spectrum is something like tinkercad.com Its a tool that runs just in your browser, and allows for lego-like construction of objects. The issue with tinkercad is that its tough to get really sophisticated with that tool, AND once you've made an object, if you want to go back and edit some sub-part of it to adjust it, it can be very difficult to keep everything else where it belonged. Fusion has a very steep learning curve, but does allow for some extremely sophisticated creation.