I don't know much about Shoreham Academy but I imagine it picks up the students from nearby Lancing, which is a bit of a dump.
There are some nice schools in Worthing - you just have to know which ones!
We live in Goring and my sons have been to both Goring First School and West Park. The former is quite small - great pastoral care. The latter has better facilities for sports and science.
Other good primary schools around Worthing are Thomas a Becket and Broadwater First.
With regard to high schools, there are several.
Durrington High School has had a lot of investment in recent years - great sports/science/art depts. - but as a result is massively oversubscribed even though it is a huge school - 1740 students. They turned away 70 children last year and my eldest failed to get in for Sept 2016.
Instead he is going to Chatsmore Catholic High School in Goring. (we're not Catholic!). Much smaller - 620 students with a focus on art, drama and music. Very polite and conscientious students when I walked round.
Worthing High School in Broadwater was in special measures a few years back but has had lots of investment. I didn't look at it for my son but have heard lots of people say how impressed they were and I think it was oversubscribed this year.
There is a new high school in Broadwater - Bohunt Academy. Bit of an unknown and they are still getting it up and running.
Two single sex schools - Davison for girls and St Andrews for boys - I was a Davison girl! Not as popular as they once were but I hear mixed reviews.
I would avoid buying anywhere near East Worthing, Lancing and Littlehampton areas. Shoreham is nice enough but there isn't much there compared to Worthing (in my opinion). I'm a big fan of Broadwater (for proximity to the Downs) and Goring (for proximity to the beach).
Hope that helps you. x