Tbh I'm way past all this. It's why you don't see me on the Latest Purchase thread. I've been fishing way too long to see any need for short rods or buckets with trays.
There really isn't that much tackle that genuinely influences your ability to catch carp imo. You need rods that can reach the area you want to fish, line that can deal with the topography of your chosen water, a very sharp hook, and a half decent bait. The rest is all just "stuff".... none of it really matters.
The way I see it the cheapest way to set yourself up is do some research and get the ABSOLUTE BEST gear for your type of angling, regardless of cost, and stick with it for many years. That might sound silly to some but saving up and spending a fortune on the best gear once is cheaper than upgrading poorer gear over and over again for 10 or 15 or 20 years (I learned this the expensive way). You'll find if you have the absolute best gear, you very rarely come across anything that's a genuine upgrade. I'll often go 2 or 3 years without any significant purchases. A few quid here and there on hooks, line and bait. Job done. I'm genuinely not really tempted by all the gear sitting in tackle shops, it's just dross that will empty your bank account.