You might want to consider brad-point bits. I have these, made in Austria, and inexpensive:
https://www.amazon.com/Fisch-FSF-13...74&s=hi&sprefix=fisch+bit+se,tools,101&sr=1-6The benefit is you can center the brad-point exactly on your mark and also not have to worry about walking. Makes a clean hole as well. The downside is they don't come in 6" (or, if when do, it's expensive). So, you'd have to drill the hole with a brad point and then use a 6" in a slightly smaller size to deepen the hole.
For 6", I've been happy with Drill America (despite the name, sadly, not made in USA).
https://www.amazon.com/Drill-Americ...s=hi&sprefix=drill+america6+,tools,318&sr=1-2No need to bother with cobalt, etc. HSS will be fine. Though most stuff at the big box nowadays has some miracle gold coating... I like Milwaukee, DeWalt, Bosch--all good from the big box.
If you do want cobalt, Norseman is a good value and Made in USA. Reasonably priced at HJE.