I'm going to suggest some more generic advice and try not to make specific board/boot/binding recommendations*. We all have personal biases to certain brands, models, or manufacturers and within each biases or preferences based upon our own riding style and the disciplines we focus upon. Good first step to ask for people's opinions but be a critical buyer, look for outside validation of opinions received here to help filter the FUD from the solid advice.
For the board, since you are a beginner I would focus on a good all-mountain or all-mountain freestyle board. Since you are still learning and will be figuring out your riding preferences, an all-mountain freestyle board should provide you the tech you require to grow and learn in a variety of disciplines. Once you get some time under your belt and experience riding groomers, park, powder, and a variety of conditions, you'll be better able to buy a second board that is more focused to your specific interests. A good all-mountain freestyle board will cover the widest possible set of disciplines good enough to let you play in all those areas. Try to avoid a park-specific board or other niche discipline board for your first board. As for length, shorter is typically associated with park riding disciplines and you lose some stability at speed due to less effective edge. Longer boards are more associated with stability at speed and carving but will not excel in park/freestyle disciplines. I would suggest you target the center mass here and go with something in the 158 range. This will give you the flexibility to expand your skills across multiple disciplines as you learn and figure things out. As for whether you should go camber vs. rocker. vs. a combination hybrid, each option will ride a bit differently. To keep it simple, camber has good pop and carving capability but can be a bit unforgiving. Rocker is a bit more forgiving and gives a bit more of a 'surfy' feel but this also comes at reduced pop and carving. A combination hybrid tries to get the best of both worlds and several companies do this very well. I can't recommend one over the other for learning as when I learned it was all camber.
(Yes, I realize that more experienced riders may disagree with my comments on camber/rocker/hybrid. I ride a combination hybrid and can carve just fine as well. I'm just trying to keep it simple here.)
As for bindings, the only exception I'm going to make is to recommend Burton bindings and I'd avoid the lower-end options like Freestyles or Customs. I rode Customs for years and when I finally upgraded the difference was substantial. Burton makes a great binding. Yes, they are a large company with huge marketing budgets to sell you on how great they are. They also have a huge R&D budget and really get bindings right. That being said, remember what I said above about personal biases. I am personally biased towards Burton bindings and they have never, ever let me down in 20 years of riding. There are good options out there though so look them over and decide.
As you've already mentioned and others have confirmed, spend more of your budget on boots. Cheap boots, or boots purchased because the price was attractive are not necessarily the right boots for you. Bad boots that are uncomfortable, not supportive enough (or too supportive depending upon what you are doing) make for a very miserable experience. The only way to really go here is to go to a good shop that has a wide selection of boots and try them on. Make sure you mention that you are a beginner and need a boot that will perform well for you in a variety of disciplines. I would suggest you need a boot with enough support to help you learn to hold your edge on heel and toe side turns but enough flex to be a bit forgiving as you will be a bit sloppy. The stiffer the boot, the quicker it will translate movement of your body to the board. The softer the boot, the more flexibility for tweaking grabs, etc., but you always interject less direct transfer of body movement to the board.
So how do you balance your budget and make sure you get what you need and stay within that budget? I would suggest spending a bit less on the board. This will be your first board but I guarantee it won't be your last. There are a lot of good all-mountain freestyle boards out there for newbies that are easily in the sub-400 range. Put the rest towards bindings and boots with boots being the bigger priority of getting it right. Think about it this way, you WILL ultimately buy a 2nd board as you grow in ability and your interests become a bit more focused. Quality boots and bindings that you purchase now will be reusable when you buy that 2nd board later. Low quality boots and bindings will be miserable now and you'll want to get rid of them when it comes time to get your new set-up in a year or two.
Or you can just be a gear-whore like me and have 7 boards in your quiver, several sets of bindings and boots, and a closet full of outerwear. Welcome to snowboarding, it is a money-pit! Haha.