Kickstart 3.1 is one of least expensive investments one can make. If you want serious Hard Disk usage, even 37.300 isn't good and I really find hard to believe that you can find easily an 37.350 Kickstart without having to ask politely someone to burn it for you.
There is nothing wrong with 37.300, the "it can only access 40 megs bug" is a falsehood, a fallacy spread on the forums over the last decade or so.
I have two Amiga 600s, both run 37.300 and have 4 gig cfcards in them, split into two 2 gig partitions, no problems at all, ran fine for years.
The only revision you need to be wary of is 37.299 which apparently lacks IDE support!