For most people interested in getting started with Cricut, I recommend the Cricut Explore Air 2.
Personally I got the Maker because I thought I would want to cut balsawood and basswood, which the Explore can't do, but I have read that those can be pretty annoying to cut - if I wanted to get serious about cutting wood, I'd probably get a membership to a makerspace and use a laser cutter instead. And as you might have guessed, I haven't actually tried any of those materials yet- I probably should have bought the Explore Air 2.
Here's the basic gist of different Cricut models.
All of these can be used without paying for a monthly subscription to anything, but you do need to have internet access when you're trying to cut - you have to be logged in and connected to Cricut's servers, because that's how they tell when a machine has been replaced by customer service and thus should no longer work. For this same reason, be wary of buying a Cricut on the secondhand market - there's no way to tell without setting up the machine if it's been "bricked" in this way by Cricut HQ and will be unusable when you get it home.
Cricut Joy - only small things, like paper cuts for greeting card-sized things. Probably not what you want for t-shirts or bigger projects, but if greeting cards are the main thing you want to make, it's a nice entry point.
Explore Air 2 - mid-range model; probably what you want, unless you specifically want the abilities to cut the extra materials that the Maker can do.
Maker - cuts the widest variety of things, including things the Explore can't handle like genuine leather, light woods like basswood and balsawood, and fabrics without backing material. You will need different blades (sold separately) for some of these special materials.
For common materials like paper, vinyl, and faux leather or faux suede, any of the models will do the job.
Explore Air 3 or Maker 3 - same as the Explore Air 2 or Maker with no 3 at the end, but can use "smart materials" to do cuts without a mat. If you want to do a lot of really big things (a single cut longer than approx. 12" x 24" counts as big here, as that's the biggest that will fit on a single mat), the 3 version might be worth it. Otherwise, save your money for materials and tools and get the non-3 version.
Cricut really wants you to think you need the Air 3 or Maker 3 - they don't even list the Air 2 or non-3 Maker on their main site when I checked today. But, you should be able to find the non-3 versions elsewhere - compare prices/sales at Wal-Mart, Jo-Ann, and Michaels. Machines go on sale pretty regularly, and sometimes come bundled with a starter set of supplies.
For accessories, you don't need to stick with Cricut brand products - often very similar quality can be had for much cheaper by buying off-brand tools. The dollar store can be a surprisingly good source of tools and blanks, though the vinyl may not be the best quality.
Things that I've found nice to have for making stuff with Cricut:
- extra mats, and especially a long (12x24") mat to make a big banner with. Get a pack that includes all 3 (blue, pink, and green) mats if you can; they are more and less sticky for different kinds of things you might want to cut.
- a tool set for "weeding" aka picking out the unused vinyl parts off your mat. This shape is the one I have and use the most.
- if you (or your giftee) has a color inkjet (not laser) printer, printable sticker paper for making stickers
- "craft blanks" is a good search term to use to find stuff to put vinyl cut-outs on - anything from acryclic keychains in every shape to artsy wooden boards to mugs and tumblers.
- Sublimation is something you can do with Cricut that's different than just cutting stuff out with one of the machines mentioned here; you don't need to buy things labeled "sublimation blank" unless you know you want to do sublimation, and have the equipment for it. (Typically, a sublimation printer, like a converted EcoTank filled with sublimation ink.)