expensive good quality bits are a good bet, not so small they snap easily.... nothing less than 5 mm IMHO.
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flatten off the end with a grinder, then a bloody good hit with a hardened centre punch, and a lump hammer, to stop the bot wandering as you get started... then slow-ish drilling, lubricating the drill bit to cool it as you go.... once you're in a fair distance, it's time to decide whther to drill out with a larger bit, or try an extractor bit.... i usually go with the extractor, judging by hand if the torque is likely to snap it... not broken one in years.... but have chickened out several times and reverted to the drill out larger route....
if access is a problem i have a half decent cordless right-angle drill you're welcome to borrow... much less room needed to get in with... although harder to keep as solid and steady ...
I have a set of larger steel bits.... designed for drilling structural steel work, but i think the smallest i have is about 8mm, maybe 10... which is almost certainly too big.
(a part of my work occasionally includes structural steel in studio builds, and hanging stuff off it , or bolting through it)
weird really.... i have almost every tool imaginable for building and DIY stuff, and Luthiery and electronics.... but bugger all for doing the car....