The schools are good, and the odds favour you. Nine in ten graded schools across Kent are rated good or better. There's a primary with the town's name over the gate. The secondary run is short enough to walk. Finding a decent school here is the easy part; the admissions letter is where it gets personal.
Ofsted has published an overall grade for 245 settings across Kent, and 221 of them are good or better, which is about nine in ten. Of those, 38 are outstanding. At the other end, 21 require improvement and 3 are inadequate. These figures cover the whole county, not Minster alone, so they describe the system your child enters rather than the building at the end of your road. Another 255 settings hold no published grade yet, which says nothing about their quality in either direction; they simply haven't been through the process in a form that produces one.
A named school near your front door is not a promise of a place. Kent allocates on its own admissions criteria, and a house can sit closer to one school on the map and still land an offer somewhere else. Check each school's own admissions rules for the year you apply, and look up its latest inspection report rather than relying on the county average, because a good county can still contain the one school you'd rather avoid.
For primary age, Minster in Sheppey Primary School carries the town's name, and West Minster Primary School sits in the same run of options, so the naming convention alone tells you where the catchment conversations will happen. Thistle Hill Academy is the other local primary families tend to weigh up. At secondary level, Leigh Academy Minster and EKC Sheppey Secondary are the names on the list. The Department for Transport's 2019 modelling puts the nearest primary about 11 minutes' walk from the average home and the nearest secondary about 23, or around 9 minutes by car. That is a school run measured in footsteps rather than fuel, which is a novelty for most of the people who moved here from further up the estuary. The remaining primaries across Sheerness, Queenborough and Eastchurch fill out the choice for anyone willing to drive.
Schools are one of Minster's real strengths: the county grades are strong, the walk is short, and the only serious homework for parents is reading the admissions rules before the offer letter does it for them.