Should I use primer alone first, or can I use paint+primer on renovated/patched walls?
Not all primers are good sealers for new drywall and tape joints. The new paint and primer combinations are great for covering existing paint, but are not a good substitute for a PVA or shellac/alcohol based primer on new drywall or patches. When sealing new drywall, it is important to seal the pores so latex/water based paints are not absorbed. Once the surface is properly sealed, paints will cover better and color will be more consistent and the finish texture will be the same from painted areas to newly primed areas. 

Here is a good article that describes the difference between different types of primers and proper selection.  http://www.finehomebuilding.com/PDF/Free/021161060.pdf