I’ve been using the same turkey fryer frame since '96. I’ve changed hoses, regulators and burner heads but the frame is built to last. And it’s the perfect height to drain wort into the fermenter via gravity. (My table was a bit short to drain the mash/lauter tun so I built a box to set it on.)
If you go that route you might be able to afford both.
+1, I use three Blichmann burners, and love them all. We even use one for 37 gallon boils. Blichmann doesn’t recommend using their burners with their biggest pot. But, I do, and it works. I get fire under the boil pot once there is about an inch of wort from the MT. By the time my fly sparge is done, it only takes another 10 minutes or so to start the boil.
I use my pump less than I thought I would. I think it depends on your system. If you are brewing mostly 5 gal batches and don’t need to get the water higher than you can safely pour it then definitely the burner.
I use my pump on every batch for accelerated chilling. That was the main reason I got it. But once I had it and it was hooked up, I found other uses for it, too.
Yes, search Jamil’s Whirlpool immersion chiller - as as a regular immersion chiller but with a short copper dip tube added to pump the wort around the coils.