There's often a temptation amongst cold-water divers to put off buying a drysuit for a while by buying a semidry. I advise against it if you can possibly manage it. Semis are nowhere near as good a solution as a drysuit, so you will wind up replacing it eventually anyway. Buying one is a false economy.
Membrane drysuits can be used anywhere from the North Pole to the Red Sea because you can vary the insulation you wear. Neoprene is more limited as its insulation is fixed. More...
Get your suit made to measure. Braces can make surface intervals a lot more comfortable - elasticated waists are nowhere near as effective. If possible, get heavy-duty seals put on the wrists.
Many people have switched from cuff dump to autodump, it's very rare to hear of anyone going the other way. Reinforced knee pads are a good thing. Avoid loose neoprene boots if possible: You should do your utmost to avoid needing ankle weights, positively-buoyant boots won't help you with this. If you suffer from cold feet, get some undersuit booties - at least you can leave these off when you don't need them.
Drysuit manufacturers with a good reputation for both quality and customer service include Otter and O'three.
Undersuit: The traditional 'woolly bear' is a dying breed in this day of high-performance fabrics. Words like "breathable", "wicking" and "hydrophobic" are worth looking out for - you want an undersuit that will keep you warm even if your drysuit floods or you sweat profusely.
Weezle have an excellent reputation for keeping you warm and dry; they can also be compressed down so you don't cook during surface intervals, and can be supplied with superb (knee-high!) booties.
However, purists insist that the only undersuits that should be considered are Type B thinsulates - available from DUI and Polar Bear. A good wicking base layer can extend the life of these type of suits by reducing washing requirements.
Make sure your diving suit is suitable for the conditions you intend to use it, is comfortable and doesn't restrict your movement. Thigh-mounted cargo pockets are worth having.
As part of the drysuit purchase, get yourself a weight belt. Or rather, get yourself some lead and a method of carrying it about.
You've got three main ways of carrying lead these days:
Belt
Harness
Integrated
Belts of 2" webbing are traditional, they're also dreadful - very few divers can claim they've never had a weight belt come undone. They're also an all-or-nothing solution, (you either ditch all lead or none) and they're not very comfortable.
You can improve a webbing belt by:
Punching holes in it with a soldering iron and threading bungee through, to ensure it is always tight during a dive.
Putting the weight in pockets so that you have the option of removing only some lead, not all
Using bags of lead shot so it's more comfortable.
Whilst most people seem to want their lead to go on their backs, you're better off leaving your back clear, and having the lead at the side. It makes it easier to reach (if pocketed) and stops your aqualung from pressing down on the lead and digging it into your back - a common cause of back pain.
A better, but more expensive, way of carrying lead is in a harness. By adding shoulder straps to the equation, it will never fall off. It also stores lead in pockets, so you can release some rather than all lead if necessary. And it spreads the strain of the lead around more.
Probably the best way from a comfort point of view is to integrate your lead with your BCD. You'll never accidentally loose your BCD, it spreads the weight out nicely, and if you use the BCD for buoyancy, it also reduces the strain your body is under during a dive: If you have 10kg of lead and 3kg of lift in the BCD, then you'll only have 7kg acting on you. If you have the same situation, but with a weight belt, you have 10kg pushing you down, 3kg pulling you up, so you'll have 13kg acting on you.
However, integrated BCDs can be expensive, make it difficult to vary where you keep your lead, can have insufficient lead-holding capacity, and can be awkward to use. You're probably best off starting with a weight belt and moving up from there when you know what other it you'll be using.
Lastly, there are some divers who consider weights on quick-release systems to be more dangerous that the inability to ditch their lead. Be prepared for some divers to have NO weight belt or harness, as their lead is all permanently bolted in place.
I use: Otter membrane drysuit, weezle extreme undersuit, all lead non-ditchable