I do not mind spending more if the extra price will result in cleaner holes. I want to make sure that the wood does not splinter.
That's not the drill. It's the property of the drill bits. The sharper they are, the cleaner the hole. The cheapest $13 drill from Harbor Freight will make perfect non-splintering holes if you get high quality bits, and let those bits do the work; you do not force them through.
https://www.amazon.com/Dremel-631-Brad-Point-Pieces/dp/B000H7D3QE
Titanium coated, good steel, and brad tipped. A nice bit for the money.
Marine Gun Builders website recommends these.
This is what you need
https://www.amazon.com/dp/B000H7D3QE/ref=cm_sw_r_cp_apa_i_gb6sFbW4AA3MC