The question of membrane or neoprene is probably THE big question in drysuit diving. Usually it ends up on personal preference and that sometimes stems from what your first suit was. I appreciate that this isn't helpful when you're looking for your first suit. So II'll give a few comparisons from my experience of having both in no particular order.
Mmbrane suits are more durable. Worth considering if you do a lot of shore diving. You can get neoprene suits that have a tough protective outer layer or reinforced knees and elbows. Such suits are not at the lower end of the market. This is not to say that membrane suits are infallible. All suits wear and barnacles or sharp rocks can catch any diver out. In general, I'd go for British designed suits for British diving.
Neoprene suits are warmer given the same undersuit. Although, you have to go for the thicker 7-8 mm suits for this to make a significant difference.
Membrane suits dry far quicker - worth considering if you have limited drying space or your storage area is not heated and well-ventilated.
Membrane suits are lighter, especially when wet.
Neoprene suits can be more comfortable if you you match the standard size or get made to measure. Membrane suits don't stretch. For this reason a degree of bagginess is built into the design. This can make them a better fit if you're not a standard size and can permit some flexibility in your own body shape over the years that you're wearing it. Some membrane suits have telescopic bodies and elasticated waistlines that reduce the level of bagginess.
I'm open to debate on this one so feel free to contribute?
Diving undersuits are teh best option for under drysuit attire. They offer great thermal protection and the good ones keep you warm when wet. However, there are cheaper alternatives for you when you're just finding out if you want to do drysuit diving. Natural fibres such as cotton and wool are not advisable as they trap moisture and keep you cold.
Katie has done some digging on the web and has pulled out some high street alternatives for men and women for under £50.
The simple answer is yes. The neoprene provides a small amount of additional insutlation over that of a membrane suit, but it is not sufficient to keep you comfortable in temperate waters thoughout the duratin of your dive.