I caution heavily against getting the most expensive kayak you can afford sentiment shared here. There are a ton of kayaks out there that are far from the most expensive and will more than do the job. There are great kayaks under $1500 after getting a paddle that are great and also offer flexibility of adding pedals or motors later on. For pond hopping, which it sounds like you will primarily be doing, a good paddling kayak will make a huge difference. A lot of the super stable boats are designed with a motor or pedals in mind so the suck to paddle. If someone says the first thing you need is a rudder I'd question two things, why is the boat designed to need a rudder and if it is a paddler issue. A well designed fishing kayak should provide stability and tracking without use of a rudder.
As far as gear goes, you can use whatever you use now with no modifications. You may have to pare down what you take if you take a lot but even then it is plenty manageable. When I am fly fishing I take up to 4 fly rods and conventional I will take up to 6. It is more about what you want it to be,
Best thing to do is see if any shops have a demo days or rental. Many shops have rentals and then if you buy the rental cost is put in to the boat. This is truly the only way to know if a boat works for you and leads me to the next piece. Once you get a kayak don't rig it based on what you have seen on youtube. Fish your kayak with your style then rig it accordingly. Many people solve problems they don't have and overcomplicate things to death. Track mounts make things much easier to mount and move things.
I have been kayak fishing 20 years and I just got a new warranty boat last year, a 2' shorter version of a boat i had for years, and I still went out 5 times before mounting anything. I currently run an ATAK120 (had the 140) and it is a fantastic paddling boat and I added a motor (NK180s) to my equipment stash 2 years ago and it is great tool for self supported river shuttles and on larger lakes.