I would recommend C24 treated timber joists from a decent specialist timber supplier. I would go for 2" by 4". The cheapest I got these for was £4.58 per metre with free delivery, so this should cost about £37 for 8 metres. There is nothing wrong with C16 for the spans that you are considering and it is a lot cheaper, but I don't like the knots, it doesn't look as good exposed because it has a wider grain and different tones. Building suppliers are notorious for warped joists because they rack them and store them in all weather. The worst I have seen is those DIY outlets that don't even sell structural timber, store their joists vertically, and then sell it on at about quadruple the cost. Online specialists are a far better choice because they are rely upon reputation, but you can go to a local builders merchant and pick out timber, cut it down and take it home if you don't want it delivered.
I would recommend that the verticals are uninterrupted and that you use butt joints with wood screws. I'm not a big fan of the 45 degree screw holes in your design, a real pain. Bolts are wonderful, but wood screws are fast, especially if you use ones with a self drilling tip. My favourites are the TurboGold plus TX double countersunk, but there are plenty of cheaper options. You need to get the right size screws to go through at least 3/4 of the wood on the back piece. If you used bolts then you could design a dismantlable stand in case you want to move house. The thing is to build something that you are going to love for years to come, and this is the reason why I make all of my furniture, plus you end up with superior quality. A strong wood glue like Vitrex wood and laminate adhesive is good for attaching side panels, but if you make it strong enough then you don't even need them. You can also use herringbone joist struts at 45 degree angles to prevent any lateral movement. I've put a picture below showing them on my gate. I think they are under £1 each and 4 of them would completely prevent the frame from moving or wobbling, even two would be enough. You can get twist nails for these struts, but any type of fasteners will do the trick. Quite a lot cheaper than panels. For the top you have a variety of options. The cheapest would be a single piece of 22mm Caberfloor P5 moisture resistant chipboard flooring. Marine plyboards are a lot more expensive but have greater water resistance. This is the kind of thing to get from a building supplier. The 18mm P5 is also good. If it looks slightly warped, don't be put off because it will flatten out with pressure and completely flatten out over time. If you are a very splashy aquarist, you could paint the top with a rubberised paint, use a bit of vinyl, or go all out and order some emperador marble tiles to give it that funky palatial look. P5 doesn't bother me when it gets wet because it will dry quickly and doesn't really have anywhere to warp if it is sat on top of a frame. I personally never waterproof the P5 because it is more likely to go to mush before it warps, which it hardly does even in the rain for days, unlike a lot of the cheaper chipboards and plyboards. The stuff is wonderful, but you might want to edge it with a nice trim strip - just make sure you glue that trim on because you don't want to see any panel pins.
Using turned wood is another idea for the verticals if you are skipping the side panels. I have used hickory balusters for my kitchen table and that has supported a lot of weight, but if you do go down this route then use something a lot stronger and thicker than balusters, like turned oak table legs. Personally I prefer the look of exposed square-cut untreated wood. Ideally you would want smooth planed C24, but C16 should be suitable if you cannot get the former smooth planed. You can customise your shelving. An acoustic box for your filter and reactor. A brass towel rack. Trimming and scissor racks. Book shelf. I always incorporate live food cultures into these designs, especially somewhere to grow California blackworms, Grindal worms and springtails. Cable trunking is also a nice touch. If you get a beer can holder, then you can put your live food in a cup with a little pipette ready to drop in live food and get some neat snappy shots of your fish. A smoke alarm underneath the tank is a great way to identify when all of that dodgy imported electronics has gone tits up. Some nice LED strip lighting can give you the rainbow puke effect, but it is also nice if you get some sound activated strips so that you can boogie out to all those old school disco classics. How about reinforced glass for the top piece, so that you can check out your epic root growth; it's the frame giving the tank strength and it would be waterproof. Somewhere for the cat to sleep? ...great plan.
The second picture below is the kind of thing that I would build. It needs a lot more work to get some nice shelving and to make it more functional, but it shows that the verticals are continuous and how to use butt joints, which is what I am suggesting. It's a box design. If you have it raised like that then you can rescue fish that have jumped, lost socks and hoover or mop underneath. The top struts aren't that necessary if you are gluing a panel on the top. I think that the box design is great, but you can narrow the bottom shelf in on the front if you want somewhere to put a stool or small viewing chair. You could go all shaker and have the stool hanging upside down. You can actually go about 50% of the way back on the bottom horizontal and fit it to the side struts, so that you have an attractive overhang, but you must never move the 4 legs inwards or it could topple. The key is to build something that you really want. I think it should cost less than £60 for all the materials (with delivery) for a very basic design. But the wonderful thing with DIY stands is that you can get something highly customised that works and looks great. It is a no-brainer if you want to go down this route. It is one of the most fun projects you can do in the hobby and in many ways you can design something far far better than any commercial stand that I have seen in recent years. The Ikea route is something that comes down to personal choice. I wouldn't even consider it as an option, but if it works for you then you've got my support. Just to give you an idea of what you can pick up second-hand: the last photograph is a solid tropical hardwood designer cabinet that we picked up for around £60 a couple of years ago. It would have been well over £1500 new, and it is 2" thick and strong enough to support a 16 stone adult standing in the middle without bending more than 1mm. They are rare finds, but they are out there, and this is the difference of what getting a stunning designer piece can do to the overall look and feel of your home.