Recommendation/advice on professionals to do ethernet cabling in existing house / preparing for UFB

I'd like to have some cat6 cables laid in our existing two-storey house (in east Auckland). Since I do not have the skills, knowledge or time to do this myself, I'm happy to pay someone to do it properly, and I'm hoping the knowledgeable folks here on GZ can recommend me professionals who do a good job. We are doing this with moving to UFB in mind, so advice on this is also welcome. Below are further details about my current situation.

We are currently on ADSL with master filter installed in the roof space of our two-storey, five-bedroom house. Our landline cordless phone is in the living room area downstairs. The ADSL jack point is located in a bedroom downstairs, which is where the modem, router and a desktop are also located. All other bedrooms have normal, working (but currently unused) phone jack points. There is a desktop in one upstairs bedroom (at the other end of the house to the router downstairs) which I'd like to connect to the network using ethernet. I tried wifi with patchy results; I'm currently using powerline adapters which work OK-ish but the connection would drop out from time to time - often OK for 1-2 weeks then one day it would drop out 3-4 times - very frustrating. In any case, since the desktop does not move, the ethernet option is by far the best, so I will not consider options such as better wifi etc.

But also we will move to UFB soon (note: we will be ditching the landline at that point), so I wonder whether it'd be better to have the home network cabling sorted before getting the ONT installed (or deciding whether the ONT should be located)?

So the minimum that I want to achieve here is a cat6 cable run (actually, I heard advice for *two* cable runs if any work is to be done) from the router downstairs up to this upstairs bedroom at the other end of the house. Since we are *not* renovating, how big a job is this likely to be? Would the roof space and phone jack points be helpful in any way? While it'd be nice to run cat6 to other parts of the house where the phone jack points are (and the TV area, which is next door to the room with the router), they are not really needed currently - the only devices that must be connected using ethernet are the two desktops, and we hardly ever use our TV these days. So if this job is complex/costly, it'd probably make more sense to only run cables to the one bedroom upstairs.

If this can be done, and if the ONT can be installed in the same downstairs room where our router is currently located, then it'd be easier to switch over to UFB when the time comes. The important things to us are the availability and stability of the connection at all times.

Any advice/comments appreciated, and I'd be grateful if anyone can recommend a good professional who can do this cabling work in east Auckland. Thanks!