Donít make it out of MDF or particle board. Both get destroyed once they get wet.
If you insist on MDF, get Medex, itís essentially a water resistant version of MDF.
I would recommend plywood. Baltic Birch plywood would be a great choice as itís also a more stable and stronger variety, as it has multiple thinner plies compared to regular cabinet grade plywood.
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+1 on this recommendation. It's a stand for an aquarium, it's gonna get wet. When MDF gets wet, it swells, crumbles and literally falls apart. When it starts falling apart and giving to pressure, there's no guarantee that it will still support your (VERY heavy) aquarium evenly, and an aquarium that is not supported evenly is very likely to start leaking or, worse, even rupture suddenly, and you're faced with a big and often very expensive mess. A MDF aquarium stand, IMO, is a commercially marketed one that you bought because you just needed a stand and it was cheap, and even those are usually protected with a faux woodgrain or solid color vinyl surface material. But even then, the water still gets under that at the edges, then it swells and falls apart. Don't waste your time and effort building one that is definitely going to have a very limited lifespan, and on top of that, look crummy the last half of its short usefulness. Spend a little more and get a nice plywood that will last you a lifetime.
As for your design, you have the top piece attached to the top of the side pieces, which seems to make sense at first glance, but it is visually less appealing unless you add a piece of trim around the top, which adds trim to your supply list, and it looks like you're going for simplicity in your design. (This goes for the bottom, as well.) I would recommend that you make the side panels the full height of the stand, from floor to aquarium bottom frame, then, with glue and screws, attach a horizontal "cleat" inside each side panel that supports the top panel level with the top of the side panels. This reduces the obvious joints that you see and makes it less visually complex. (The more visible joints there are, the more it appears to be "pieced together" from scraps.) It also adds to the side-to-side stability of the stand through a more complex joint than a simple stacked joint that is more prone to folding over and collapsing. (Of course, the back panel on your original design would likely prevent that, but every little bit helps.) Even if you choose to leave the top panel resting on top of the side panels, use a cleat in the corner for stability. Also, make your side panels the entire depth (front to back) of your cabinet instead of allowing the edges of the back panel to show. (Again, fewer visible joints.) You could, of course, make the door cover the complete width of the stand, with the appropriate hinges, but if you do that (instead of having the door recessed between the side panels) you will probably want the top panel to overhang the front edge of the side panels by the same thickness of the door so that the door doesn't stick out and look odd. (If you choose to recess the door, you may consider using a thin "piano hinge".) Instead of having a solid bottom piece directly on the floor, I recommend letting only the side panels rest on the floor and support the weight. This way, you can raise the bottom panel a few inches above the floor and attach it by the same method as the top (with cleats), and use the unused bottom panel as a shelf inside. (You will also appreciate being able to have more access beneath the stand whenĖnot "if"Ėyou overfill the aquarium!) The front top panel (above the door) will not really be supporting any major load, because the vast majority of glass aquariums, unless they are HUGE, can actually be supported by only the corners, or, if over ~4' long, possibly with a middle support as well, but even that may be unnecessary because the bottom glass is supported by the side glass via the silicone seams. So, unless you just like the thin horizontal top/front piece, the entire front panel could be the door. If you want to take your project to "the next level" without a huge added expense, you can purchase an "edging" veneer/tape product that can be simply ironed onto the exposed plywood edges so that the layers in the plywood don't show. It's fairly easy and really makes a simple plywood project look more professional.
I hope this gives you some ideas to think about, so that you can build an aquarium stand you will be proud to show off, and that will serve you well for many, many years to come.