A great starting place for anyone wanting to investigate Scott is the 'Boy Child ' compilation - it is out of print, but can still be picked up cheaply - it only covers up to 1970, but what a collection!
If you are looking to investigate Scott 'post 60's' you should probably avoid most of the solo output until 'Climate Of Hunter' The one exception is 'til the band comes in' which certainly has its moments.
First stop - the track 'No Regrets' from the walker brothers re-union album of the same name. You'll probably be familiar with the song - Midge Ure did a cover in the 80s for one.
After that - the four 'Scott' tracks from the Walker Brothers 'Nite Flights' most notably 'The Electrician' Listen to that one and tell me Sylvian wasn't a fan.

'Rain Tree Crow'
Climate Of Hunter onwards, through Tilt & The Drift, I'd find it difficult to pick out individual tracks to recommend as what would appeal to one person would almost certainly turn someone else off. You should be aware that somewhere along the line Scott (mostly) changed his vocal style. He now seldom sings in his 'crooner' style, preferring to emote in a higher register which can sometimes seem a little strained - however....
Climate Of Hunter - Suffers a little from 80's production, but features some notable guests - Mark Isham and even bloomin' Mark Knopfler puts in a good turn (on the cover of 'BlanketRoll Blues'). 'Sleepwalkers Woman' is probably the stand out track for me, very slow and elegant, I can hear the seeds of Tilt in there.
Tilt - Well, if people had ignored 'Climate Of Hunter' (Virgin's poorest selling album ever I believe) that wasn't about to happen with Tilt - it got a lot of press - much of the popular press going 'WTF!' It is a sensational piece of work - uncompromising, strange and beautiful - listen to the opening track 'Farmer In The City' If its ominous tones appeal, buy the rest of the album. Expect tiny noises and walls of sound - this is uneasy listening at its finest. I always think 'Bolivia 95' wouldn't be too out o place performed by Rain Tree Crow.
The Drift takes the sound ideas of Tilt and extrapolates them. Wierdly some people who love Tilt can't stand The Drift and vice versa - personally I find them to be fairly close cousins (albeit born more than a decade apart.) Purchase if you like the idea of sides of Beef used for percussion. Don't get me wrong, it's fantastic stuff, just I wouldn't pick it as a starting point for most people.
If you yearn for the Scott of old, then even here you can be satisfied. He has contributed to a select few soundtracks - generally in the rich woice of old... 'Man From Reno' from a Toxic Affair is great - it's probably on one of the podcasts on my website somewhere, but I can't remember where. 'I threw It All Away' from 'To Have & To Hold' is a beautiful Lushly orchestrated track - worked with Nick Cave on that one. He also collaborated with David Arnold on the Bond Film 'The World Is Not enough' 'Only Myself To Blame' is the track you are looking for. Then there's 'Pola X' soundtrack to the film of the same name - I always think of it as a kind of extension of Tilt as it contains some elements from that album, but it does stand on its own too.
It's worth hearing some of the (little) stuff he has produced or written for others - Pulp's 'We Love Life' is one of their best and Ute Lemper's 'Punishing Kiss' is quite interesting - also featuring work from Nick Cave, Elvis Costello, Philip Glass, and Neil Hannon,
....and for completists only... 'Darkness' from 'Plague Songs' a jolly ditty from a collection of songs about the ten Plagues of Egypt described in the book of Exodus. Oh, and the afore mentioned '....And Who Shall Go To The Ball...'
Does that help? No, thought not. Summary - 60's solo - classic. 70's solo mostly poor and out of print. 80's solo - interesting. 90's solo - Genius. 00's solo continues to be peerless.
Sonic