Most of the steels I've heard of have been answered for, more or less...however, I'm wondering where 1055, and Busse's INFI, fit on the scale.
Also, which of these steels will not rust?
Thanks!
From the top of my dome - guys, feel free to correct/add:
Most steels will rust to some extent (even stain-less is not stain proof). H1 and titanium are two examples that are used for rust 'proof' blades. I've never owned a titanium blade but I understand that often it doesn't hold an edge that well. H1 is not heat treated, it is work hardened by a rolling/grinding process and is used (amongst other steels) by Spyderco and Benchmade. I have a Rock Salt in H1, it takes a good edge and has reasonable impact resistance, edge holding is mid tier but not great (can't have everything!

); that said, its edge holding should improve with repeated sharpening as it work hardens... not sure what that means for its impact resistance
Most 'stainless' steels that are used in knife making have >10-11% chromium AND have to be able to take a decent to good edge and be not too brittle (nb - in the early days of VG10 and S30V there were a lot more reports of chipping but that seems to have diminished as the heat treat protocols have improved - I have multiple knives in both these steels and love them) and retain that edge (where some of the alleged super steels are better) and be easy to maintain/sharpen (this last one is one of the reasons why Buck still uses 420HC, and they seem to have its heat treat pretty well sorted).
Infi, I've never owned a Busse but it is hard not to be impressed by the love its fans have for it. Busse (and it's related 'Bussekin' companies) are the only one to use it and apparently have a very involved proprietary heat treat (40-50 hrs??). It is not a stainless steel per se but is stated to have a reasonably high degree of rust resistance for a non stainless carbon steel, it is said to have excellent impact resistance with the edge tending to roll rather that chip - so you can 'steel' it straight, without losing as much material as if you were sharpening out chips. Reportedly it has great edge holding also. It is the balance of its edge keeping and impact toughness (as well as reasonable rust resistance) that seem to have delivered it so many fans/HOGs. There has been a thread in the last 24-48 hrs in the Busse manufacturers section that discusses how rust resistant it is. There are too many threads to mention that describe its impact resistance and edge holding. Have fun looking through the Busse section of BFs, some of their thread are hilarious (in a good way). Unfortunately, the sticking points for most people are 1) price and 2) the way blades are released onto the market (1-2 models at a time, if you miss that run it may never be repeated and you will have to pay quite high prices on the secondary market). Ahh, one day...
1055 is a mid carbon steel, can rust, being mid range in carbon it has good impact resistance (not too brittle). I've never owned a 1055 chopper either

so I've not got first hand experience of it's edge holding compared to high carbon steels - but I would expect it to be less impressive in that regard.
Again, I hope that takes more mud out of the water than I've put back in.