What should I consider when cutting a dryer vent hole?
In general, the shorter the vent, the better, so moving the dryer next to the basement wall would be the optimal solution.  If you can't do that, then moving the vent as you said would be a lot better than your current set-up.

This article covers the whole topic in a lot of detail, see especially the sections on why to keep the length as short as possible: 


Dryer Vent Hose Length Considerations
Dryer Vent Hose Lengths: Keep it Short


Running the vent to the new location shouldn't be a problem; my preferred tool for cutting the hole would be a hole saw, but they can be expensive.  Looking at your photographs, it seems like don't have any plumbing or electrical stuff to complicate the job.