This is jumping right into the maelstrom! If there's one topic which has been guaranteed to get people arguing - and bitching - furiously, it's this. So be warned... disagree with pleasure, but no nasties please.
Basics? You need one if you are to get close to "that sound"... or at least, your version of it. You can actually get away with the basic tap tempo echoes included in the Vox VT series if you are not concerned with authenticity. Problem is that, as heard on the records, the echoes - in addition to having a "tone" of their own - are unevenly spaced. Check this...
This pic and lots of other echo related stuff from the excellent Echotapper site (http://www.echotapper.nl/)
And if you check the other recorded tracks you'll hear differently spaced echoes. So you need something which will allow you to space the echoes unevenly (or better still, buy something with the work already done?) The best budget buy at the moment is definitely the Yamaha Magic Stomp which (I think) is discontinued, but there are still quite a few floating about, and if you want the job done for you Charlie Hall (good name for an echo guru... it sort of reverberates) can be contacted here http://charliehall.proboards.com/index.cgi and he will sell you a file to give you all the Shads echoes in one fell swoop. (He also programs Quardraverb Q2 and Q20 under the name of Echoes from The Past as used by Hank on Shads tours and recent recordings)
"Ah but you mentioned tone earlier?" And that's really why other current modern machines don't get a look in. They'll conceivably give you the echo, but they can't give you the degraded and wobbly sounds of an old vintage echo unit which is what we're looking for, but the Q series and MagicStomp can... with one exception. I'm currently experimenting with a Line 6 M13 Stompbox Modeller which allows infinitely variable echo spacings with up to 7 heads (with a bit of fiddling) and the ability to emulate tape wobble etc... and you can add studio reverb as per KonTiki and Midnight too if you so choose... first results are encouraging... and, of course, you get all the other effects too...
And, of course, there are the excellent TVS echoes from Australia... http://www.tvsspecialtyproducts.com/ only hampered by their cost when imported into Europe... In effect more expensive than the vintage units they emulate... solid state.
And in the UK ESE Echomatic http://www.echomatic.co.uk/... valves and real wobble!
So why not buy a vintage Meazzi, Vox, Binson etc? Well you can, from about £600 for a Binson, through to £2000 for a Meazzi, but, unless they've been faithfully reconditioned they can be very unreliable...
Now you'll find people very inflexible as to what they recommend in this area, and each will swear blind that all the others are talking nonesense, but, based on my own experience and ears, here's my recommendation...
Unless you're playing for discerning Shads nuts, the basic Vox VT tap echo will do just fine. I defy anyone to prove to me that average club/theatre audience can tell the difference.
I've heard excellent results from the Yamaha MagicStomp and you can edit the parameters on your computer to your heart's content adding wobble etc ad infinitum.
I've owned and used an EFTP Q2 for many years and find it to be excellent - still around second hand but some now suffer from duff batteries and displays as a result of age. Have the advantage (or disadvantage if you're a twiddler) of being able to switch straight to a whole range of preset Shads echoes with no knobs to worry about.
I currently also use an ESE at home and find that excellent too... (and I'm told that there is virtually no difference between its circuitry and that of a vintage Meazzi)... lots of knobs to twiddle...
I still have an old Binson tucked away (currently for sale in our Marketplace) and I used to have Roberto Pistolesi's Meazzi...
Now, I'm ducking already, there are those who will tell you that the only way to get "that sound" and in particular, those echoes is to use the old kit. But my own experience and listening to others using it just doesn't confirm that position...