If you come over before the actual rent starts you will, by default, have no access to the building and the apartment. So first thing to do is make sure you do by arranging that with your regie/landlord.
Getting your B permit early would require you to register when you arrive, at which time (if you came a month early) your 'real' address probably wouldn't exist yet. Why the hassle? If you arrive a bit early you could do so as a tourist, no?
Electricity, waste disposal, warm and cold water, and heating are the landlord's and the commune's job. You can rely on that working when you move in, though making sure a few days ahead of the move won't hurt. Days, not a full month. As has been mentioned you'll get to chose the source of your electricity but you will be supplied before that already, nothing to sweat on.
In case you don't know: Tap water here is the same quality as mineral water, it just lacks the bubbles.
As for internet access, in Zürich city you generally have these options, though not in every house/street:
- fiber provided by the city Elektrizitätswerk (electricity company). Getting connected takes about four weeks. Check availability for your building here
- tv cable, assuming your house/apartment is connected. Ask landlord/regie
- ADSL (phone line), provider is your choice. Connection speed depends on your subscription. Getting connected typically takes a couple weeks
- by radio relay (Richtfunk) provided your apartment isn't shielded/blocked by some other building. See www.antanet.ch if interested. However, this option is fairly unknown, and with fibre arriving that may no longer make sense.
With fibre and ADSL you only have a line, a connection, but no data feed thus you'll also need an ISP, some of which also offer packages with tv, phone and mobile. With cable and radio relay the line and the ISP are provided by the same company, they are one package. Not sure if it still applies, but just a few years ago UPC Cablecom (provides cable access) ratings for service quality and customer service were nothing short of abysmal.
You'll also need a mobile phone provider. In many cases this can be combined with the above. Swisscom has a reputation for excellent quality - you'll most probably overpay compared to others but, especially as a newly arrived who barely knows his way around here yet, it may still be your best option.
PS:
Ordinary search on this forum is less than useless, use google powered only