For sightseeing in Amsterdam and traveling to Brussels, should we stay in Amsterdam Centraal area or can we stay at Sloterdijk station area?
How difficult and expensive it is to travel back and forth from Sloterdijk to Amsterdam Centraal?
It's quite easy to travel between Amsterdam Centraal and Amsterdam Sloterdijk. Trains are frequent and the trip is about 6 or 7 minutes. The base fare is €2.30. The travel time to Brussels is slightly less from Amsterdam Centraal because the direct trains to Brussels do not stop at Sloterdijk.
Most tourists will want to spend more of their time closer to the center of the city, though, so it's probably only a good idea to stay near Sloterdijk if your accommodation is sufficiently less expensive, or if you have something specific you want to do in the area.
Staying in the central area, inside the canal rings, let's you easily walk central Amsterdam and for me that works better. I love walking the central city.
The travel angle is well covered in the other answers. From the tourist angle, I would say, it depends on what you like and want to do.
If you are the 'dinner, short travel, bed' kind of person, Sloterdijk is not bad.
But on the other hand, if you are a 'dinner, roam around, visit place to drink, visit place to listen to music, wander slowly to hotel' a central Amsterdam location will be better.
I would not even advice the Centraal Station area, but more near the Leidse plein area or around the places you will find your choice of music if not there.
Travel time to Amsterdam Centraal Station will be about the same as if staying close to Station Sloterdijk but your travel time and more importantly the ease of getting back to your hotel in the evening will make the difference.
Both areas will be safe enough, also late in the evening, but depending on the actual time of night, can feel a little deserted outside of business hours (Sloterdijk) or shopping hours, (Amsterdam centraal).
There will be public transport but the night trains do not stop at Sloterdijk, so from about 1:15 to about 5:15 you will be restricted to night buses. And those are on a one per hour schedule as far as I have found.