My advice would be not to buy anything at first—check your local library for the books on this list. You’ll probably find Boutell, Fox-Davies, Neubecker, and Slater, and probably either the Parker or Woodward-Burnett glossaries in most good-sized metropolitan area library systems. I’d recommend getting your bearings with those and whatever else is in the collection, finding out what your particular areas of interest are, and then decide on that basis how to allocate your money.
By the way welcome (Failte) Rob.
One comment about how I started when bitten by the heraldic bug I just started to buy books and have never stopped buying. Do visit antiquarian bookshops, most of them have a book or 2 on the subject and sometimes for very decent prices.
Canadian heraldry Proficiency Courses - Resources
RE: Joe’s question about "Harald the Herald"—its been a few years but I did see it once in the kids section of our public library. I wouldn’t include it in your list unless you have a special "for the kids" category or some other way to indicate the intended audience. Unlike "Simple Heraldry, Cheerfully Illustrated" - which is a joy!—my recollection is that H-t-H is a bit content-light.
Yeah, as it happened, I was in a library last night where it was on the shelves. The author expresses indebtedness to Fox-Davies, whom she (?) describes as basically the ultimate authority on the subject. And the text reflects that.