I wondering if I need to have a precision notched straight edges, nut files and fret files and what else?
Not right now.
While a shopping list of tools provides some reassurance for one's anxiety, it's also all based on "what if." I urge you to refrain from filling up a shopping cart until
after you've inspected your new neck and then determined what you need.
You may feel that, for your playing style and preferences, you don't need to do
any fret dressing. I've never bothered with any of my WM necks while I'm sure that'll make a few community members' hearts palpitate.
You may find that the slots in the nut are dialed in right to where you want.
You may also find that once you receive the neck and inspect it, something isn't quite right. You might contact WM customer service and after working through it with them, they offer a return/exchange, maybe. Then the replacement turns out even better and might not need any of these adjustments. You never know.
The tools mentioned are good to have, but unless this is going to be a regular thing of multiple necks (and not just from WM) over time, then spending anywhere from $150 to 200 and up may not make as much sense for a one-time use.
Add to those tool costs the risks of inexperience. It may be less costly in the big picture to take the neck to someone who already has those tools and the know-how.
However, multi-purpose tools like a power drill and a set of drill bits are good things to have around just for the versatility around the house. Mine are used frequently, for guitar work, for house repairs, for construction, etc. Notched straight edges, fret rockers, fret files, radius gauges, feeler gauges, and nut slot files are (mostly) purpose-built and specific to guitar work. I have them because I
do use them on a regular basis, either for my own guitars and basses or friends' instruments. But my friends don't, because they know they can come to me and it's cheaper for them than buying the tools themselves.