The short answer:
Go for a Hardboot 

The long answer:
A hardboot skate has a removable liner. This means that the padded part of the skates can be taken out and replaced. Softboots do not have removable liners.

Some of the cheapest skates on the market are softboots (do not get those, they are horrible) and also some of the most expensive skates on the market are softboots.

Skates should NOT flex sidewards at all. The stiffer a skate is built, the better it performs (stiff on the outside does not mean it is not comfortable on the inside).

Some of the most stiff skates in that regards are carbon based softboots like the Seba CJ, Powerslide Evo or FR SL. They are however all over 400 euros. The cheapest way to create a well performing skate is to built it in the hardboot style.