With a heat press you have 3 main options for making shirts:
1) Heat press vinyl (HPV) -- best for solid, simple designs with a minimal number of colors. Produces a result similar in appearance and feel to silk screening. Pros -- Fairly simple process if you already know how to cut vinyl Cons -- Can be pricey as HPV runs right around 5x the price of Oracal 651. If you only plan to do one color, then it's not so bad - trying to do a 3-color logo on 100 shirts it starts getting crazy. Best for short-runs of a shirt/hat as silk-screening starts becoming cheaper once you pass a certain point. Requirements -- vinyl cutter, heat press, heat press vinyl, protective cover sheet, cotton or polyester substrates (hats/shirts/etc.) - can do other fabrics with different varieties of HPV.
2) Inkjet transfers -- best for multi-color or photographic designs on a wide variety of fabric types and colors. These are basically the iron-on transfers that all of us remember from growing up. Pros -- They work on most common fabrics and are available for light or dark colored shirts. Cons -- Requires a little more care during washing/drying to prevent fading and cracking. Requirements -- Inkjet printer with pigment based inks, transfer sheets, heat press, protective cover sheet, cottor or polyester substrates. Optional: vinyl cutter for contour cutting to remove excess border
3) Dye sublimation (technically it's inkjet sublimation, but almost no one calls it that) -- Best color matching and allows you to put images on a lot more than just shirts. Pros -- no noticable hand (feel) to the image - the dyes bond to the fabric and have no rubber or stiff feel like many iron-on transfers, can do coffee mugs, dog tags, cutting boards, phone cases, koozies, and hundreds of additonal items. Cons -- Really only works on 100% polyester materials - can be used on 50/50 poly/cotton blends, but will be very washed out and will fade, high temp inks are expensive compared to normal inks. Requirements -- Inkjet printer compatible with high temp inks (Ricoh or Epson), heat press, protective cover sheet, transfer paper, polyester substrates.
Based on that, from where you're at now (have a cutter - buying a heat press), your cheapest option is HPV as either of the other two options also requires an inkjet printer.