I'd still replace the brake cables - modern ones are way better than the old ones. For friction downtube shifters then a modern linear gear outer will give a slightly more positive feel but is definitely not important.
It may be good to have all the parts ready but it may be more costly. I would wait until it arrives and have a good look at the bike. From personal experience (and many here know) I tend to buy too much - with a 'just in case' mindset. The downside is that this proves costly, the upside is I end up with plenty of spares.
Regarding where to buy, what to buy and how to buy - this is difficult. Once you know EXACTLY what you need, you can shop around. As with everything, if you want something special, it will cost more. Something special will almost always be slightly more difficult to source. If it is a build like the one i am doing (one of the ones i am doing) now, I am cleaning and greasing and replacing defective parts on a Raleigh ProRace. This is a cheap bike and deserves cheap parts << that may be an unfair statement but it does not require an Anniversary Campag Groupset - if that makes sense.
I had not expected to spend anything on it but inspection revealed a couple of items which needed replaced - headset and BB. I would normally put a new chain and cables on a bike as a matter of course. And, dare i mention (hides head in shame) pedals. The bike needs new ones.
So, HS came second hand from RB, BB came from Chain Reaction - Shimano sealed BB, I had cables - available from LBS, pedals came from ebay.
It is possible to do a full one stop shop in Chain Reaction, Wiggle, Evans, Ribble, apologies to those i have not mentioned but for some older or more specific items they may not have anything suitable. Then i would resort to SJS Cycles - they had a load of spares for older parts and a good selection of newer parts which can be used on older bikes (does that make sense?). I have not checked but an example may be a 5sp freewheel - does CRC have them?
Really the world is your oyster, there are other cycling forums where you can buy stuff, but tread carefully who you buy from, if you have any doubt about a seller do not buy! You SHOULD use PayPal protection for purchases - this gives you protection from fraud. I think there is more info about this in the sales section.
Finally, have a good look around RetroBike - bike sales, components sales, wanted section and this will give you a guide of what is available and some idea of prices too. If you need help sourcing a particular part, post a message and someone will help out or give you a pointer.
Probably the last line is the most important... after all that typing!!! I hope the bike arrives safe and sound - obligatory pictures must be taken to track your build. And if there is one thing that helps when posting anything - IT IS PICS - everyone loves pics!
As the first poster said, welcome to the Money Pit! I refurbed my first bike last year and as far as budget goes I'd say think of a number, then double it and you'll still be nowhere near!!!!
My experience taught me to get to know the guy in my LBS, he was a lifesaver. He had parts in his loft that I couldn't get online, or they were going to cost a fortune. To be honest, he was glad to get shot of most of it!
If you're in no hurry then bide your time on the for sale section on here - it's far cheaper and more friendly and personable than eBay, and you'll get good advice to boot. There's always some nice stuff crops up for not very much.
If you've got one of those 'Recycle Your Bike' places locally they are also a great place to find old bits n' bobs.
It's a steep learning curve - I soon realised how important it was to have a set of vernier callipers (Aldi have then for £6.99 for a digital pair at the minute) and to know about threads, OLNs, etc etc. The list is endless! And I won't even bore you with my 'WTF did I cut my steerer too short' tale....
Having said that, you're at the right place for advice. Good luck with it, it's a great way to occupy your evenings....