The two biggest for me are the obvious looks and price, obviously I have to like the way it looks, and it has to be in my budget.
After that it's the steel used (and the quality reviews of the maker regarding said steel is taken into account, though sometimes with a grain of salt);
I prefer stainless over non, not that i dont respect good simple "carbon" steels for whay they are, and they certainly have their place, but growing up on the shore and building docks (on the saltwater) in my younger days, i earned a valuable appreciation for stainless over non as I've seen rust, and I've seen RUST! (Even on stainless).
That said, despite their "more resistant" claims, i cant stand overly soft blades either that i have to sharpen because i sliced through the air to fast. I like balance. Ive never tried H1 but from the reports i dont think id like it much despite it being rust "proof".
the lowest grade steels I'll even consider are (in order)
440(a) (Mainly because the production methods are usually questionable by almost everyone who still uses it)
7cr17mov
Aus8 (some people really like it, i ve never been impressed)
Often these alone will break the deal for me, anything lower certainly will, as even with these I have to really like the knife design and see a really enticing (sale) price to bite.
420 by anyone other then Buck hc is a no go, 5cr or lower, a no go, aus6, not interested, if someone gifted a knife of any of these steels my way, I'd regift 'em to someone in need of a blade more then i, who doesn't appreciate better quality steel composition.
Most budget steels I own are 420hc (Buck only)
8cr13mov (or better Chinese grades; 14mov+ or 9cr, etc.)
Or 440c, which done well I absolutely love! I'll almost never pass up a good deal on 440c, always on the lookout as I actually prefer it over some of the "super" steels even.