C24 will come from colder regions like Scandinavia where the wood grows slow and dense. C16 can come from anywhere, but in recent years the quality has gone downhill a bit. Non-structural timber is probably alright for smaller stands, but I have seen poor quality timber split badly from places like Homebase. All timber merchants will import into shipyards and from there it makes it's way into merchants. At this point the timber is usually kept dry and laid flat in warehouses so it is very straight and in great condition. There are then three kinds of retailers: Builder's merchants like Travis Perkins and Huws Grey will usually transfer the timber directly to their outlets. It is often laid on rack systems, sometimes the wrong side up as people fumble through it, and usually is exposed to weather. In those conditions it often has a tendency to warp and you can travel from outlet to outlet trying to find good pieces. It's not such a problem for 8" joists, but get progressively worse when you scale down. They will have plane cut and sometimes rough cut joists. You rarely get either of these structural timbers smooth planed, but they will do non-structural indoors (untreated) joists with this smooth finish and in good quality, which costs a few pennies more. The untreated structural timber they will usually put outside because it will not rot. You just turn up, cut it down, fill your car and you go and pay. The second type of retailer is a DIY outlet like B and Q or Homebase. They transport the wood from the merchants warehouses to distribution warehouses and then on to shops, so there is an additional leap, and I imagine they don't pay much attention to transporting it because it is often chipped or scratched. In all of my experience they rarely ever have structural timber, and most of their timber is usually extremely poor quality and badly warped due to being stored vertically on a slight angle. The quality is awful sometimes because it is not properly pressure treated or aged (lots of sap) and they really are at the bottom of the food chain. The big difference with much of their timber is that when you drill into it it will hit knots and fragments will come away or it will split down to the cut when you pre-drill; and that what they sell is really very expensive for what it actually is. Even their floorboards can contain metal fragments which blunt drill bits. It's a pot luck situation but is usually not worth the visit; saying all that, I have had some very nice smooth timber from these places on odd occasions. Wickes probably fit into this category although they also do mail order, the jury is very much out on the quality of what turns up at your door: far better build quality and cheaper but sometimes warped or damaged. The third kind of retailer is a UK-wide mail-order "specialist" supplier. They will transport the timber from the importers (merchants) warehouse to their own warehouse where they will store it flat and dry, sometimes without props to keep it very flat and straight. The quality of these joists can be superb and usually these retailers will show a photograph of the batch to highlight the excellent storage conditions. It is not uncommon for them to use air conditioning and to pick-out sub-standard timbers because they value their reputation, and they will often pick the best timbers for carpentry from each batch if you ask them. They charge a bit for delivery unless you have one locally, which you should because most timber arrives from ships to ports on the east coast. They are usually cheaper than the other two kinds of retailers, and you can often pick up special dimensions or particular planed joists like smooth planed C24 or bevelled edge timber because they are often linked to reputable sawmills with surplus bespoke stock. They also have access to some of the nicer coniferous species like certain pines. Often too they advertise on Ebay, which is handy if you want buyer protection. The fourth option is a timber yard (sawmill) where they either import and saw timber or specialise in UK grown lumber, which can be sawn to your specification. I do not really rate most UK softwoods, but they often have a broader selection of hardwoods, and I have even managed to get 10 year-old air-dried UK native Elm which is now virtually extinct. The problem is that sometimes they do not cure the timber properly and it is not always certified as structural, which doesn't matter that much for a small cabinet, but if it does start to warp as it air dries, then you are treading on ice. They are however a great place to pick up English oak and Scottish pine and you can usually walk around to see how they produce the timber. They are sustainable and support the local economy but can charge a premium and aren't very common in your region unless you want hardwood, but they can cut to size if you want a flashy top piece or solid-piece doors with natural staining patterns.
For what you are making it probably doesn't matter that much which you choose because the weight is not a major factor, structural or non-structural (not that relevant if you have 6 legs), treated or untreated, but I do think aesthetics are a major factor. All timbers have a certain look and this is especially true with different softwood species. I do like the design you linked to. For something like that, I would choose a variety of different woods for different sections, that could mean using something like maple plyboard for the doors, oak trims and mouldings and hickory legs. Saying that, spruce looks great when it is unfinished and it is really cheap. Some woods costs is a bit more, but not that outrageous if you look on Ebay. Luckily, oak trim is now very common and you can get a wide variety of prefabricated doors or plyboards with different woods, but both cost a bit more. Alternatively, I would be tempted to go with glass doors and a reinforced glass top. If you are working with solid boards then note that some hardwoods can be very difficult to cut at home, like English Elm, which cuts well along the grain, but is really hard across it. The design you are looking at is a lot more difficult because you need those 45 degree pocket holes for the screws, also, personally I would not choose to cut the horizontal spans, but it's up to you. I find it hard to get the perfect angle with 45 degree pocket screws and I don't trust them as being as strong, there can be splits as you tighten down, and they take more time than self-drilling wood screws. I'm sure it would be plenty strong enough anyway if you chose them. The problem with getting certain standard trims and mouldings is that they can look very generic and a bit boring, which is why I would shop online. I also prefer hidden hinges or brass fittings. I would go for some nice mother of pearl knobs or possibly marble ones. I think that you might as well design it for a slightly larger aquarium. That could fit two 40 cm cubes, also a 80 cm tank with a nice ledge, but it's up to you. I like enough room for a cup of tea by the side. Overall, nice design you have chosen. I wouldn't feel too pressured to buy from any particular timber seller because there is an awful lot of choice, but equally you can make something quite standard if you like the style.