There isn't really a better setup using your existing equipment.. all you would need is some quality heat transfer papers and a heat press.. both you can find fairly cheap.
the method you use for printing is slightly based on the logo. if you have like an 8 color logo you probably want heatpress or
DTG. but if its a 1-2 color logo i would suggest screen printing because IN MY OPINION it is better quality and can be done very cheaply.
Take a look at the prices and it might be worth it for you to have it screen printed. If you like to do stuff yourself, go for the heatpress. Ask around and search the form for some quality papers and go for it! good luck.