What papers are suitable for markers?
I'm not sure what you're defining as "normal drawing paper" or "sketch paper," but you can ultimately use markers on any surface, however you will experience different results depending on the qualities of the paper.

Weight

Markers will generally soak into the paper and bleed to some degree (with some brands tending to bleed more than others); working with a thicker paper like bristol or watercolor paper will tend to resist bleed-through better than thinner papers like newsprint.

Tooth

You'll generally get a smoother result with a smoother surface, though depending on the result you're looking for, you may like the look of using a paper with more tooth to it. Experiment here to see what you prefer.

Coatings

Some papers (marker pads, for instance) will be coated to prevent bleed-through on a thinner sheet; this can allow for better workability in blending, but may also result in less saturated colors as the ink cannot soak into the surface. This can also create issues with layering multiple colors or extensive blending; again, this may come to personal preference and style.

Absorption

If you're planning on extremely heavy blending, particularly using water and water-based markers, you may wish to consider a paper that is better suited to heavy water applications such as a smooth watercolor paper over a lighter paper that may warp or disintegrate when saturated with water.

Bleed

You may also wish to experiment with the amount of bleeding your chosen markers will exhibit on different papers. All markers will bleed to some degree (except, possibly, on coated papers), but some papers will wick the ink away from where you deposited it more than others. You'll want to find an amount of bleed that works for you, and learn to work with it as you're drawing.