Whether you build your rack maximizing vertical or horizontal space is largely personal. With BP's you don't need to worry about them being hard to get back into the uppermost boxes since they are slow moving. I had a vertical rack that I kept arboreal racers in and the snake in the top box could be a nightmare.
Heat distribution is a concern with vertically-oriented racks but there are always ways to deal with this if they fit your other requirements.
Regarding horizontally-oriented racks, I believe your biggest concern should be whether or not you can fit them through a doorway. Typically they are taller than most doors are wide so flipping them on their side is not a realistic option. For BP's most breeders use fairly long boxes so again the width of many racks won't fit through some doors.
First decide on what box you will use. If it's long and your doorways are narrow you should build your rack vertically.
If horizontal will work, they do make for a nice work area on top and it is easy to check on your snakes.
My last thought on this specific question is that you only need it to hold 8 boxes. If your boxes were 6" tall, your rack would only be less than 56" tall. That's not much to worry about. The biggest worry would be utilizing material well. Most lumber comes in 48" increments so a 56" tall rack *could* waste a lot of material. On that thought alone I would lean towards a shorter rack that was four tiers tall and where each shelf held two boxes.
$200 may be tough if you want to use a big box. If that includes the price of the box it will be very difficult to meet that price. Your cheapest option for material would probably be MDF coated with rubberized contact paper. I line even my melamine racks with contact paper since it resists humidity so well. It is also easy to replace.
Regarding heating issues, I'll leave that to other people on the forum. If your room is fairly warm already you might be able to get away with just some rope light for heating. If you need night-time heat they now make red rope light which filters out most visible light. Rope-light will be your cheapest option, whether it will provide enough heat for your application is hard to say. You could control it with a rheostat (as you could heat tape) until you have enough money for a thermostat.
To conserve material/save money you could build a rack with a fairly open design. I'll post a picture of one of mine. If heat retention is a concern the gaps could be filled with with cheap styrene insulation. This design also saves on weight.
Another design that utilizes material well is the one pictured on the ballpython.ca site.
Here's my cheap rack that I threw together one day to quarantine a group of Gonyosoma. I think I only used 1 sheet of plywood ($28) and two rolls of contact paper ($3 each). The screws, nails, and wood glue was stuff I already had.
For another $10 I could have filled in the gaps with 3/4" styrene insulation. The rack was in a heated room so that was not necessary.
