The best calculator for GCSE, IGCSE and A - Level is the Casio FX 991 Es Plus.
It can solve quadratic and simultaneous equations - simple for GCSE and IGCSE, integrate between limits and differentiate - good for A - Level, and has normal distribution functions built into it - good for A - Level S1.
It also has a general equation solver. This makes it unnecessary to rearrange equations in order to make a particular variable the subject 0 useful for when using the Sine and Cosine Rules.
It only gives numerical answers and does not perform symbolic manipulation, which makes it exam legal for all GCSE and A - Levels exams where calculators are allowed, and is only a step up, and slightly more expensive for the more commonly used Casio, so students should not find it hard to learn how to use.
More advanced calculators that thus are bricks, have long lists of functions to scroll through to perform often simple calculations, and are so complicated as to be next to useless.