Nordman fir is the best one to go for - very low droppage and a lovely shape. They tend to be the most expensive ones, but worth it.
We usually put ours up the first weekend in December and it lasts fine until Christmas, but I like to get it up early and down early so I always have it down in advance of New Years anyway, by which time it is usually looking a little tired. If you want it to last into Jan then I would say to wait and get it a week or two into the month.
Where are you getting it from? We go to one of the local forestry commission forests and pick our own - if you are doing this then the best time to go is first thing in the morning as you will get the freshly cut trees and plenty of choice before other people have spent the day hoking through them all and leaning them against each other at awkward angles.
If you are picking it yourself then ask them to cut a bit off the bottom for you - this does two things - firstly, it helps to keep it fresh. Where a tree is cut will always seal up again with sap fairly quickly so if you get it cut just before you leave (or cut it yourself when you get it home) and then get it immediately in water it will drink more and will stay fresher for longer. You can also prolong the life of your tree but putting some wee nicks in the side of the trunk at the base of the tree below the water line - do this every few days and again it will help it stay fresh as it keep a lifeline for water open. You will generally see that a tree with drink loads in the first week and not much after that. The other thing it does is make sure you have a good shape of tree. Often real trees can be a disappointing shape when you are used to a perfectly shaped artificial one - they are often spindly at the top and sparse at the bottom. We generally go for about a foot taller than we need and then cut a bit off the top so that we get rid of the most spindly bits and it looks fuller at the top, and then also cut a bit off the bottom (and often some of the bottom branches which can be easily damaged in transit) so that we don't have a massive gap at the bottom.
If you have a radiator near where the tree will be just turn it off before you put your tree up as it WILL kill it quicker - trust me - I know!!! The most mess actually comes from removing it - dragging it back out through doorways when it's no long wrapped up tight and when the needles are dry does make a mess, but by that time your house is clear so you just do one big hoover then and it's fine. Last year we were able to buy a big bin liner type thing to wrap around the tree when we bought it - it was specially for when you needed to take it down. We had a wide, 10ft tree so it was enormous, and not something you would buy from a shop, so I'm hoping we can get one hit year too. Another alternative would be cheap plastic floor covering which you can buy from B&Q for when you are painting - if you wrap the tree in that and wrap it with masking tape or something before you take it out of the house it will minimise the mess.
We have always had real trees and our kids have always been quite good around them - just really strict from day one that they weren't to touch it and it's never been a problem. If you are wary of your little one going after it, could you get a mini tree for them - a cheapy artificial one (think £10 in B&Q) which is just the right size for an 18m old and then let them decorate it themselves and call it "their" tree. Put a few wee presents around it too. I know someone that did this when their DC were little and it has become a really nice family tradition. (I'm kinda jealous actually that we never thought of it or did it actually) Their DC are now 13, 10 & 6 but they still do it with a tiny wee tree and they love it. They used to put wee presents underneath when the DC were small which they didn't mind them opening (usually just empty boxes etc) because they knew that the appeal of the tree is often the gifts underneath! Very quickly the DC would "wrap" up their own toys and books to put under "their" tree - it was really sweet. My friend used to also randomly hide little treats under the tree for the DC to find - so they used to look every day and they never knew whether they would find something or not - nothing big, just those wee christmas freddo bars, or a couple of chocolate coins, or a Christmas DVD she'd bought cheap which they would watch later.
Anyway - that was a total essay and probably not what you were expecting when you asked about which real tree to buy! Sorry!!!