If you are new to speed cubing then a good budget cube is the best place to start. Don't worry about magnets and lubricants!
Take a look at the MoYu Meilong 3x3 or QiYi Warrior S 3x3
Now you are looking for something with a bit more spice! Why not take a look at a magnetic cube?
Take a look at the QiYi MS 3x3 or MoYu Meilong M 3x3
A premium cube is perfect for competitions. These are the best of the best!
Take a look at the GAN13 Maglev Frosted 3x3 or GAN 12 Maglev (Frosted)
There is a range of larger cubes available from budget to premium magnetic.
Larger cubes add that extra challenge you've been looking for.
Take a look at the selection of unusual puzzles and shape modifications!