Brand New Ball Owner

[LittleTreeGuy]

Couple of things.... some others have already said....

1. Your heat mat (UTH) NEEDS to be regulated. You can use a dimmer switch (available at lowes or home depot) or the best solution is a thermostat. Spend the money and get a good one now. you won't be sorry. This may be the single most important investment for your snake. Herpstat 1 would be a great choice. The Herpstats are great products.
2. You don't need a water bowl big enough for him to lay in... so he can lay in it. If your bp is soaking in his water bowl, there are likely problems such as mites. Now, that being said, since you have an open tank, the bigger water bowl, the more humidity. With a screen top, you'll need all the help you can get. I would look for something at least 6" in diameter and 2" deep.
3. Feeding bucket. not needed and I would suggest against it. You want your snake to feel comfortable at all times. A happy snake will eat. If you move him to a new environment, his first reaction will be fear. That will only work against you in getting him to eat. The "feeding aggression" some people associate and try to avoid by feeding in a separate tub is a myth. If you feed your bp regularly, there won't be any issues. Just feed him in his tank and it will be easier for both of you.
4. Feeder size - I recommend buying a small kitchen scale that will weigh in grams, up to 2000-5000g. That will let you be able to weigh your snake occasionally. If you know the weight of your snake, you can find out if you're feeding enough or too much. A snake should eat around 10%-15% of their body weight each meal (at least until they're adults, then it will cut back a little). So, if your snake weighs 100g, you'll want a mouse around 10-15g. If he is young, you're probably fine with mice hoppers for now but will want to move up in size soon. They grow quick when they are young.
5. Hides - I think it's ideal to have identical hides... one on the cool side and one on the warm side. If they are different types, the snake may favor one more than the other, and in turn, may want to stay in that hide and not move when it needs to be warmer or cooler.
6. As you alluded to before, you'll want to cover as much of the top of the tank as you can. Plexiglass or aluminum foil is good for this. Whatever you can get to keep the humidity and heat in the tank. Just don't put anything meltable or burnable near your heat lamps on top if you have them.
7. Lights... some people use lights for heat. that is fine for the day, but snakes need darkness at night. You're better off just using a CHE for heat around the clock. THey put off heat and no light, so they're great at night.

Most importantly.... welcome! It's a lot to take in when you're starting out... but you're asking questions so I see a happy future for you and your snake! Best of luck!!