Lurchers are any Sighthound crossed with a working breed - so essentially a herding breed or terrier. Sighthound to Sighthound crosses are officially Longdogs, but the term is rarely used these days. Sighthound cross terriers are sometimes referred to as Whirriers! 
As first time Lurcher owners I would avoid anything with too much Saluki in. They are beautiful dogs, but fairly unique in their behaviour, independent, strong willed and recall is more likely to be an issue than with other sighthounds. Bedlington terrier crosses are gorgeous, but can have a stubborn streak a mile wide and are very lively as youngsters.
My boys (pics on profile page):
Lurcherboy - (the grey/blonde scruffy lad) Deerhound/Saluki x Greyhound (or poss Whippet as he has short legs for his mix) /Border Collie. He is an absolute sweetheart, gorgeous gentle nature, good recall (unless he's found something disgusting to roll in and he's only started doing that now he's hit the grand old age of 9). You wouldn't really know he has Saluki in him, but then it's only one of 4 breeds in his mix and clearly not dominant from his appearance (see profile pics).
Pip - (the red and white one) unknown mix as dumped at birth, but most likely a lot of Greyhound, with some Wheaten or Irish Terrier and some Border Collie. I would say he's probably multiple generation Lurcher to Lurcher cross, so no breed is particularly dominant. Again, he has a really sweet, gentle nature and excellent recall and he is really easy to train, whereas Lurcherboy, bless him, is not the sharpest tool in the box!
As for where to get one. I would register with Lurcher Link and EGLR, then frequent the EGLR FB page and LL homeless hounds page and apply for anyt dog you feel may be suitable. LL will take your details and bear you in mind when/if any suitable dogs come up - not sure if that's how EGLR work, but do know they are careful to match the right dog to the right home, so you may have to wait for the right one to become available, but it will be worth it.