2 year old gives you more options, as you don't have the worry of transferring in.
If you go with Trafford then you need to consider catchment areas closely AND be aware of the grammar school system in Trafford.
Many kids are tutored to get into the grammar schools and the grammar school system means you don't always get the closest high school. It's really competitive and getting more so.
If you don't get into a grammar school some of the comprehensives don't have a great reputation. I know that because of the way they've allocated this year, there's one area which ended up outside the catchment for the most local high school, with a bunch of kids instead being allocated Broadoak in Partington which is a real trek. It's also not got the best reputation, so they parents have kicked off. They won't get anywhere because the schools are all so over subscribed in Trafford ATM.
The schools outside Trafford don't do the 11plus. You can opt to do it and some people do travel in for the grammars but it's much harder to get in to the Grammars if you are outside Trafford now.
But there are some really good high schools just outside Trafford, which don't have the same pressure to get into because they don't have to do the 11plus. You DO have to consider the catchment area and be in the right primary school for some of those though!
So my advice is definitely to do your research carefully if you don't want to move again at a later point (potentially needing a primary transfer in the process). Do you want to go through the stress / cost of tutoring? Do you want a single sex high school? Or do you want to hedge your bets on schools and go outside Trafford into areas which are slightly less diverse?
There are some very nice places in the wider area to live, but it really does depend on what your biggest priority is. If you are looking at the Trafford area, a budget of £500k is starting to look on the tighter side too now and you may find yourself having to consider compromises on location/size (again look at those catchment areas). Just outside Trafford was generally more expensive but this has changed in recent years - largely driven by the demand for grammar schools and better public transport.
You will have to compromise on something at some point if you are set on this area.