During the takeoff roll you should run the check
ASI alive and climbing appropriately
RPM max, engine smooth
Oil Temp and pressure green.
(maybe try remembering ARO -like an arrow)
If any of these is not OK abort. If the ASI fails during X-country I would look for the nearest suitable/long runway and approach keeping speed up. (You don't want to try a short field approach). Navigation should not become a major issue -I'd consider maybe using ATC for vectors and PAN you need priority over other traffic as you need maximum attention on your flying, getting down without a low altitude stall is critical. During instruction I spent some time flying base/final with my ASI covered, its surprising how this focusses you on correct feel/sounds of the plane. A slow turn to final has killed many pilots so a straight in approach could be best.
I'm not an instructor, but that is how I was taught.
Hope this helps.
Cheers