So are you talking about inkjet printing heat transfers?
Or are you trying to screen print?
I know I will be hated and flamed for this, but even tho I am new to printing on my own... I have dealt with printed merchandise for 14 years (I know that is nothing compared to some here)... and in my experience... I have never seen a heat transfer from a laser or inkjet hold up like a screen print. Ever.
I know technology has come a long way, but still.... even the new transfers I have seen do not hold up to regular wash and dry.
(But I will say, I have no experience with vinyl transfers, so I cannot speak to those)
I have shirts I did in 2003 that have been through 100's of wash/dry cycles and they are still 100% intact. Screen printed.
Transfers work. Just depends on what you want.
You said a heat press, and a 16" x 24"... not sure what you mean by the size.... ???
A heat press can be used to cure, yes. I forgot to mention.
It is not a bad method really.... I am actually gonna grab a shirt press very soon...
I want it for a lot of things, but in doing shirts, where I can cure with my dryer... I can opt to cure with the press, and depending on what I use to top it, like a teflon sheet, or baking paper, and when I pull (hot or cold), I can get a shiny print, matte print, even an orange peel. That is some insane versatility that you can't accurately control with a dryer. Not that it is better than a dryer, just good for it's intended purpose, should it suit your purpose.
So many options.
Sounds like you have a decent handle on where to go, but when you are talking about something like this, I would say double your figure and dive in

it's a forever, never ending cycle of madness once you get in.
Just like automotive/hotrods/boats... women, or the crazy relationship with THAT one, music, radio control, bands, art, computers, a house, whatever the hobby... anything....
But maybe that's just my OCD