-5 or 6 levels
Assuming you want a tub that is not excessively deep, this should be easily accomplished in a 4' tall rack. Since lumber tends to come in 4' increments this is good. Will help you save money.
Tubs that are around 31/2'x 2'x1/2' in dimensions
What species is this for? One problem with the super large tubs is that they are a bit more fragile than regular tubs. So you build a rack system around them and by the time the boxes start to crack they are discontinued and you rack is useless. I like the Iris boxes for large tubs racks because the boxes are very tough. I use a large Iris box in my racks and they are great.
Another problem you need to consider is the actually floor area of the boxes. With the thick rim around the top and the sloping sides there often is not much floor space left. That's why I asked what species this is for.
There is the Iris CB-110 tub at about 39"x20", but I think the Iris CB-75 at 22"x37" would be even better. Both are available from ReptileTubs.com. Great guys, great company.
Can have heat tape or mats added
Is this part of your $250 total? Regardless, adding it later is no big deal. Although you might want to account for it now if you prefer having it recessed into a groove, etc.
Not sure on wood (melamine, ply, etc...) Suggestions?
3/4" melamine for the shelves is hard to beat, despite its weight. You can use 1/2" plywood for the sides and leave the back open to save on weight.
Looking to spend around 200 - 250 on this project
I think this is doable. If for that price you need to buy the heat source and thermostat then you might have trouble.
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Current snakes:
0.0.1 Gonyosoma oxycephala - Java locale (green)
2.2 Gonyosoma janseni - Seleyar locale (all black)