Typically I would recommend buying a wetsuit first, because a well fitting suit will make the most noticable improvement in your diving comfort, and is the most problematic to rent. In this case, since you're going to Cozumel in the summer, the water temp will be 84 or warmer, and you need to decide whether that means a full suit or a shorty. I would say probably 60% of the divers I see in Cozumel year wear 3 mm full suits year round, but I really prefer a shorty in the summer. Shorty suits are a lot cheaper and easier to fit as well, so you would stand a better chance of getting one online; I spent $40 for a good one from a place that deals in close outs of all sorts of outdoor equipment. If you get cold easily and want a full 3mm suit, it's definitely worth buying it locally to get it to fit. Fit is by far the most important thing about a wetsuit's performance, much more so than features or fabric.
If you end up in a shorty, remember that you'll still need a full suit someday unless you're planning on limiting your diving to really warm water.
Many, many divers in Cozumel rent regs with computers on the console, so I would see no need to buy a computer at this time. If you do that, try to get the same one for your trip so that it tracks your N2 loading throughout the week. If you take a day off from diving, you can go to a different computer. The most important thing would be to use the same computer for a complete day; i.e no diving in the morning with one computer and in the afternoon with a dfferent one. Although the idea about using tables has some merit at least theoretically, there are a few practical reasons to use a computer in Cozumel. One, and this is important IMO, a computer will give you an accurate and immediate ascent rate indicator. You're going to find that controlling your buoyancy in blue water with a current is a whole new challenge, and the computer can help you, especially in situations like holding a 15 ft safety stop when you have no immediate reference for your depth. Another thing is that you'll be diving in a group in which most others will be using a computer. The typical Cozumel dive profile is multilevel, often these profiles violate PADI tables. A very typical 1st dive would include a maximum depth of 70-80ft, then usually a slow ascent to 50-60, then 30-40, then a stop, with a bottom time of an hour or so. After an hour SI, a common 2nd dive would be an hour BT at a max depth of 50 ft, usually leveling off at 35-40 ft for the latter part of the dive. Run those profiles on the PADI tables and see what you get! Sooo....if you're diving tables, you end up with a choice; violate the table or leave the group, neither of which is a good option. You could request, and probably receive, a separate DM to dive table-friendly profiles, a an extra cost for less bottom time. You could also buy the PADI wheel and plan your dives, but overall in this situation it's easier and overall safer IMO to just use a computer. Save your table diving for situations in which A) you can dive square profiles and B) you're not in a group with a leader that's building the profile around a computer's ability to process multi level dives.
If you want to buy a computer, and you want to go cheap, try to find a used (or new if you can find one) Aeris atmos 1, but don't spend more than $100 for it. I can already feel the flames of everyone saying it's crazy to buy an air-only computer, and if you can afford a nitrox computer, fine, but you did say "budget" and there are lots of decisions to make about a computer that you might not be ready to make. Finding the cheap atmos 1 will get you through this trip and several more for a very low price, at which time you may be ready to learn nitrox and you'll have the experience you need to buy the computer that's right for you. There's a huge difference in some computer algorithms, so it is a decision worth waiting to make.
