Does a mechanical keyboard make you faster?
Not automatically, but it offers better tactile feedback. Each key has a distinct "click" that confirms the keystroke. This physical feedback helps the brain develop muscle memory faster. On a membrane keyboard, the feel is mushy and uniform, making it harder to tell if the key was properly activated.
Which switches to choose for typing?
There are three major families. Linear switches (Cherry MX Red): smooth travel, no click, fast but less feedback. Tactile switches (Cherry MX Brown): small bump at mid-travel that confirms the keystroke, excellent for typing. Clicky switches (Cherry MX Blue): bump + audible click, maximum feedback but noisy. For learning to type, tactile switches are the best compromise.
What budget for a good keyboard?
A decent membrane keyboard costs 20-40€. An entry-level mechanical keyboard starts at 50-70€. A good mechanical one runs around 100-150€. Is it worth it? If you type several hours a day, yes. It's an investment in your comfort and efficiency for the next 5-10 years.