Assuming that you want to print onto cotton then sublimation is not a viable option (although there are some sublimatable vinyls around they are not particularly good).
For printable vinyl solvent print is the obvious choice. Shouldn't fade and will last as long as the garment. Printer costs are high, with the cheapest starting at around £5k (Rolnad BN20), but you can also print signs banners and stickers.
There are also laser transfers that work better than inkjet transfers. They dont last as long as solvent transfer. There are some cheaper desktop laser printers that will work, but if you want a really good A3 printer with white toner you are looking at around £6k. Transfer paper can be expensive.
If you are thinking of either of the above methods then in terms of outlay you are getting close the the price of DTG or DTF.
A good DTG printer (direct to Garmet) will cost around £10k+.
A good DTF printer (direct to film) will cost about the same (£10k+), although I can see that coming down over the next few years.
In terms of controling how your customer washes the garment all you can do is place washing instruction clearly on the garment neck label or on a swing ticket.
You could always outsource your transfer production to someone with a dtf printer. It will increase your costs per garment slightly, but you will have no capital outlay.