This is definitely the start of something cool, but for me the combat atleast in the browser version felt a bit too slow. I think all the player melee attacks could be twice as fast and it would be a lot more enjoyable imo.
Also some more indication of a hit on the player could liven it up a bit. Perhaps when the player is hit have a faint red screen flash or something. Actually I think in general the health counter could be more obviously a health indication by maybe moving it into one of the corners of the screen and maybe add a little plus icon next to it. I thought it was the number of enemies I had to kill at first.
I like the idea of the store but I think perhaps rather than having to walk into it, either make the player have to press a button to open the shop, or as the previous suggestion said have the shop window come up automatically between rounds. Almost every time I tried to get out of the shop I had to back away first and then close the shop window otherwise it would open right up again.
I think you're onto something though, wave based cactus defence could be fun with some more polishing up!