Also, do check catchment areas. We moved house (because of ds's job) when ds1 was 1 year old. We didn't really think about schools, apart from noticing that there was a primary school opposite the top of our road - literally 1.5 minutes walk from my front gate - and we were very shocked to find that, despite our proximity, we weren't in catchment!
Apparently, because the school was so popular, the local authority had decided to slice off some of the catchment area, and transfer it to another school - and for some obscure reason, instead of taking a slice off the edge of the catchment area nearest to the other school, they took a wedge which centred on the original school. 
We appealed, mainly because of the proximity - I believed it would be absolutely ridiculous for me to have to walk past the school I could see from my front door, in order to get to another school, just because of a daft catchment area division - and we won our appeal.
But for ds2 and ds3, we didn't have guaranteed places, because they were out-of-catchment siblings. They did get places, but it was a lot of stress.
To answer your original question, if you are moving house, it makes perfect sense to look at schools, and make sure you are in catchment for a school you like.
That is what we have done when we have moved house (or considered moving house) since the house move described above. We moved to Scotland 5 years ago, and we did look first at schools - finding good schools for the dses was our priority - and when we found a senior school with an excellent reputation that we believed would best suit the boys, we went out that same day (we were on a house- and school-hunting visit to the area) and rented a house in catchment for that school. We made it clear to the school that, although it was a 6 month rental, that was not because we wanted to trick our way into the school, but because we wanted a rented house whilst we sold our house in Essex and house hunted for a house to buy in catchment.
We could have submitted an out-of-area request, but as there was only one place left in ds1's year, we decided to go for broke and rent the house in catchment - after all, we were only renting a few weeks earlier than would have had to anyway.