If you can find one, an L39 or L42 Lee Enfield would be the cream of the crop, and likely put you back a few thousand dollars should you ever find one for sale.
Pre War NoI MkIIIs with the magazine stops and older windage adjustable style sights is a must for any serious lover of Lee Enfields. One thing to be careful about is many of the adjustable windage sights were pinned into place to stop them doing that and if you force it, you will break the rear sight. Then the long range volley sights. A real rifle.
Lithgow no1s are also rather nice. You can find many WW2 made ones used by the aussies, and come with gorgeous wood.
If you can find one of the Lithgow No1 snipers. That too is pretty rare and wonderful in everyway. Behind that is the No4 snipers that are a little more common, but has a real bad problem with fakes.
No5 Lee Enfields are rather nice, but cost quite a bundle and once again many No4s got cut down into fake ones during the 50s and 60s. Rather stout to use however.
The No4s are awesome. I much perfer the peepsight over the others, but that is personal preference. They have a heavy barrel and wonderful in every way. In the US you will pay a premium for the Savage built ones, much like in Canada the Longbranch ones cost more. My best No4, is a No4 Mk1* Longbranch that I use for competitions and hours of fun.
For a really good shooter, look for an unissued No4 Mk2. They are much rarer nowadays and come with beech wood, instead of the walnut of older rifles, but tend to have perfect barrels. I am still on the look out for one of these for my collection.
We can't forget the Ishapore 2a and 2a1 in 7.62mm Nato. Sure they don't have the refinement, but they have a far commoner round to use.
There are so many Lee Enfields that they are all real wonders. Just keep an eye on the quality. In the past I paid anything from $40 to $250 for various versions and there are some real bargains out there.