UTP cabling is an infrequent, but regular, topic of conversation here. You might care to browse for some old threads.
AVF Mantra for UTP cabling is two "always run two" along any given cable route. It's highly unlikely that a UTP cable will fail in service, but if it does and you have no alternate in situ, you are off the air until you rip and replace. Depending on the cause of failure, if you have an alternate, you stand a chance of getting something up and running sooner. It's surprising how often one finds a use for "just one more" later on. The additional materials cost of the extra cable is low compared to the hassle of installing it. If nowhere else, then for your switch---switch interlink. So doing also will facilitate use of a technology called "Link Aggregation" to increase capacity in future if ever you find a single ethernet link hasn't got enough bandwidth (not that that's likely any time soon in a SOHO use case.)
While you are renovating is the ideal time to think holistically about cabling. For example, is now the time to add some additional runs for Wi-Fi Access Points, extra telephone extensions, web cams, doorbells, alarms and anything else you can think of. And if it really is a full house rewire, consider getting "something" to all rooms even if you have no present need. Might as well do it now (once and for all) while the house is a building site. When planning this sort of thing for "office" type environments, I used to put in loads unless there was serious budget constraint - though of course you have to draw the line somewhere.
Newbies do rather tie themselves in knots "worrying" about what "cat" cable to use. There's much more to achieving a given "cat" of install that what cable you buy. IIRC at cat6a, to actually be cat6a, it all has to be installed in "proper" "containment" (trays, ducts, and so on) and most SOHO installers aren't going to do that. cat6a is also usually (electrically) "shielded" and all that shielding needs to be bonded to earth. The professional cabling installers that lurk here may have more to say on the subject.
Ethernet does not work any "better" because you give it higher cat cable. I wouldn't bother with the higher cat cable - I'd use cat5e or maybe cat6 if the cost difference wasn't that big. Both of them are good for gigabit (1000mbps) ethernet up to 100m (further sometimes, though that's outside spec.) and 10Gig to shorter distance, though probably more than enough for a SOHO.
To actually "be" cat whatever, all the installation stipulations and working practices must be observed (which get more and more stringent as the cat gets higher) and the thing must be tested with some very expensive test equipment, well beyond the means of you average DIY'er or sparky. (But that doesn't mean it won't "work" - it's pretty hard to get badly wrong - poor termination it the worst culprit.)
Many basic electricians may be happy to run the cable for you and may even terminate it (it's not hard) but data network cabling is a specialist skill. Which is why getting professionals to do the work to standards (the "cats") costs more. You might care to explore with your electrician where his expertise/competence level is with this so you "know what you are getting." A properly installed cat6a deployment would be presenting you with a sheaf of documentation showing that each lobe has past certification and testing (you get a page of graphs for each lobe!)
Label each cable lobe both ends with a unique number. It's surprising how fast you forget what goes where. You could also record this in a "patching schedule" - some people include diagrams and records of what cable was used, when the work was done and how it was tested - even if it's just a basic continuity test. It's all useful information for future owners.
A Patch Panel (PP) is "just" cable termination - same as the wall boxes in the rooms, it's just more of it in a concentrated form factor. An ethernet switch is what "joins" the cable lobes together to create a LAN. (The LAN ports in your SOHO router are a built in ethernet switch.) If you deploy a PP, you still need a switch to create the network.
As others have commented, solid core UTP cable forming the permanent infrastructure is normally terminated onto faceplates and PP's (the IDC "punch down" blocks on the back of both are identical) and patch-cords are then used to take the link from faceplate/PP to the "active" equipment. So in your comm cabinet you "patch" between the PP and co-located switch, (or ay other equipment in the same locale.)
If you are going to put active equipment in a "cupboard under the stairs" - the heat can build up a bit, especially if there's no ventilation, the space is small and "other" - er - "junk" the gets piled up on top. Just be aware of it in case you need to take "measures" subsequently if it gets a bit toasty. It's not he worst idea to get in there a blow the dust out the gear occasionally. Even though my NAS is in the living room, (in free space,) I've just given it it's annual "dust" and it surprising just how much had accumulated in the grills and inside the case!
Here's a link to my favourite DIY site on UTP. Doubtless there's plenty of videos on YouTube showing how to do it.