Hi and welcome to the site!
I'm another vintage Raleigh fan - I've got three vintage Raleighs and another two in the process of being built up gradually. I think that Raleighs of the 1980's are hugely under-rated bikes.
Before you spend a whole lot of cash rebuilding this bike, have a bit of a think about why you are doing it. If you want the satisfaction of rebuilding a bike and making your old treasured machine look like new again then don't let me stop you, however, if you want to end up with something like a mint condition Raleigh Wisp then save yourself a lot of hassle and buy
a new-condition one online. The Wisp isn't a high-spec machine (although I do understand it's still a nice bike!) and
emotional attachment aside, it probably isn't worth spending any time or money restoring a ratty one.
Assuming you do want to rebuild it though (and it's a lot of fun!) you're going to need a few specialist tools to get it apart and you might think about buying these while the weather is preventing you from stripping it down. One thing that you'll certainly need a
crank extractor (obviously shop around).
You're also likely to need a tool or two to get the bottom bracket off depending on what type it is, as well as a large spanner and/or vice to get the non-adjustable cup out.
A set of allen keys will also be a requirement.
In terms of sourcing components, you might find it is cost-effective to purchase a second Wisp (or other '80s bike) to raid for parts - this is a technique that I've used several times in the past. If you want another set of the Stainless Steel Weinmann mudguards then you can either pay through the nose for a second hand set on their own or buy a whole bike with them on. They were often also fitted to Falcon bikes of the same vintage. These are pretty heavy though and chromoplastic ones are a lot lighter. Extra points can be scored for sourcing an original 80's ESGE set ;-) One of the arts in vintage bike restoration is to buy a parts bike, take the parts you need and then sell what's left for the same amount or more then you bought it for!
In terms of buying new components, it all depends on how far you want to take it. The Wisp originally had a Sachs Hurett gear system which was fairly widely used and is easy to find second hand, it also had Weinmann brakes and IIRC a Raleigh Custom crank set. If you want to keep it relatively original-
looking then source replacement '80s parts, and there's opportunity for some weight-saving and performance-enhancing upgrades. Look at the groupsets that the more expensive Raleighs had and perhaps look at fitting those instead of the original kit. Something like a Sugino crankset, Campagnolo Record gear systems, lightweight Sakae seatpost and stem..... But bear in mind that you're bolting it all to a relatively heavy frame so don't go too mad.
If you're anywhere near Cambridge you're welcome to take a look in the parts bin in my garage - there are quite a few old Raleigh bits in there!!!
Have fun...
PS forgot to mention: Wheels.
IIRC, the Wisp originally came with 27 x 1 1/4" chromed steel wheels. You can still buy this size of wheel but tyre availability is not as good and choice is a lot narrower than the current 700c standard size. As an aside I always think you can tell the quality of an 80's Raleigh bike. If it's got the chromed steel wheels then it's usually a lower-spec bike but if it's got Weinmann alloy wheels then it's usually more upmarket.
Anyway, the point is that if you need to replace the wheels then you've got a few choices to make:
Option 1: Buy 27" wheels (might as well buy alloy ones!)
Pros: Originality, brakes will still line up, like-for like swap so you can use your existing rim tape, freewheel, tubes and tyres
Cons: Old size, poor tyre choice
Option 2: Buy new 700c wheels with hub that accepts screw-on freewheel
Pros: Good tyre choice, wider choice of wheels
Cons: You might need to exchange your brake callipers, screw-on freewheel is old technology
Option 3: Buy new 700c wheels with freehub that accepts cassette and lock-ring
Pros: current technology, lots of choice in tyres and cassettes etc.
Cons: You might need to exchange your brake callipers
If you go with option 3 then bear in mind that there are two types of free-hub and the Shimano one will give you a choice of cheaper cassetttes...