I'm in the process of seting up a home based recording studio. I have a
simple question. In your opinion, is it cheaper and easier, to have a
analog based or digital recording studio, as far as. should I have a
mixer connected to my computer and have all plug-in's on a recording
program, or is it better to set every thing up, and have a room full of
racks.

There are about 50,000 answers to that question, most starting with "Go with
digital, but..."

The three most important equipment categories to any recording studio are
the mics, preamps, and monitors. Generally those should represent about 80%
of your budget. If you go cheap on those, all the fancy hardware and pretty
software in the world won't fix what they lack.

Starting from scratch, look into Rode mics, FMR RNP preamps, and research
the hell out of monitors, find a set that lets you hear the most subtle
changes to a mix, not just a good sounding speaker. Some folks mix great on
a $300 set of Behringer Truth's, some can't settle for less than $1800
Dynaudio's. Find out where you fit on that scale.

Revisit the overall system configuration once you figure out how much money
you'll have left, and the types of recordings you'll be doing certainly
comes into play. Accommodating drums doubles the cost of the hardware, for
example.