Do you definitely want Brighton, or just to be in that train line? We lived in Brighton when DS1 was small, and although it was great in terms of baby groups, meet-ups, things to do, we needed to live practically on top of the station to make the commute easy. It’s over an hour to Victoria, and from where we lived in Hannover, plus his onward journey in London, it was easily an hour and half plus each way. He was out of the house just after 7 and rarely back before 7/7.30, and that was before allowing for delays.
Your budget will also be fairly limiting. You will get a 3 bed with a small outside space, but in the areas you can walk to the stations from, they won’t be huge.
If you are not wedded to the idea of Brighton, you’ll get more for your money a bit higher up the train line, making the commute much shorter. Places like Burgess Hill/ Hayward’s Heath are generally better value for money and you’ll be able to easily get into the catchments for the best primaries (some of which are very good), and be within walkable distance of the stations. They do, however, have a very different feel from Brighton, so it depends what really matter to you.
If you are happy for a longer commute, places like Worthing are much more like Brighton, but it’s quite a trek into London.