Depends on your budget, where you're looking at moving, why you're moving (City work, suburbs family move - very different locales to consider) etc. There are gigabit FTTP deployments in the city centre (Kings Dock et al.) and basically the entire city and outskirts all have Virgin Media available. VM locales with Gig1/gigabit available will have better broadband infrastructure than those without (i.e. older network kit and lower speed tiers up to 500Mbps available). At this stage tbf I think basically all of Liverpool is Gig1 capable.
FTTC/ADSL wise it's more of a gamble. The exchanges are few and far between, so without FTTC you're looking at woeful ADSL speeds. If the property is close enough to a FTTC enabled cabinet, you'll see better speeds - but in my experience the cabinets are generally full and there's no capacity to get a new install. My house has a FTTC possibility and the cabinet is fairly close, but again no capacity so I'm "stuck" with Virgin Media or else plain 2Mbps ADSL.
If you can get into a development (basically flats/appartments) with Hyperoptic or Vodafone Gigafast you're laughing. Virgin Media 1 gig cable a distant second. Anything after that don't bother, essentially. Find properties first and THEN enquire about broadband. It's impossible to list the entire infrastructure and local variability of service quality for a city this big.
