MONITORS I Am Puzzled

However by being limited by using a Telcel phone on a computer line I am crippled as far as doing fast searches

Given this a faster laptop won't help. It will help for offline for offline processing.

Based on this thread you need connectivity to the TV or monitor and readability, not high processor speed. A store manager might say no to trying your laptop while if you asked the floor person he might be willing. Provided you have the cables etc and they think you'll buy so they get the commission. Worth trying. Or try a computer repair shop and explain your case. I'd be very familiar with all of the PC options to change font type size and screen size and prepared with some text files.

Any friends in SD that could help with some tests?

Others keep suggesting a TV which is fine if the resolution is adequate for you. Video is one thing and text is another relative to clarity on a TV in my experience.

Whatever you buy will have some resale value down the road if no longer needed.