After the first one I think this is my favourite of the Hammer Draculas. has some very nice touches. On the whole, of their gothic horrors I prefer the Frankensteins to the Draculas. The first two are excellent, as is Frankenstein Must be Destroyed. Frankly John, if you have only just discovered the pleasures of Hammer you are in for a treat as there are loads of very enjoyable films for you to discover along with some very corny schlock (which can of course be just as much fun).
Col. Mortimer's comments re Amicus is also very valid. They were Hammer's biggest rival and put out some excellent stuff, especially their portmanteau films with 4 or 5 short stories in one.
I would also recommend their psycho thrillers. They made a bunch of black and white ones in the early sixties (The Nanny in your box set would qualify in this category as would Taste of Fear recommended by Yodlaf) and made a bunch more in the seventies in colour. I thoroughly enjoy all of them. The black and white ones have a nice stark quality about them and the colour ones have breasts. What more could you ask for? Oh, and while we're on the subject, their Lesbian vampire flicks from the early seventies are also well worth a visit.
Truth be told I can't think of many Hammers I haven't enjoyed to some extent or another, even the genuinely bad ones, so any list of recommendations from me is likely to be very long and unwieldy but, to start with, you shouldn't go past the two films Brian Clemens did for Hammer. Captain Kronos and Dr Jekyll and Sister Hyde. Both are a lot of fun and the latter is a work of genius (in a bonkers high camp sort of way).