Question
My yard is completely covered in Henbit weeds and clover and god knows what else.  Where do I START??  
In particular if I decide to use a Spectricide or Round up that attaches to the hose - will I want to cut the weeds with a lawnmower first so they chemical get to the root or is that more dangerous because it stirs up the seeds???
Any advice on where to start would be appreciated.....

Answer
I take it that your plan is to replant the lawn - sod or seed.
The operations are: reduce weeds, install (or check) irrigation, sod or seed.
Roundup?is an excellent non selective, post emergent weed killer.
For best results, apply it on young, actively growing weeds. Sometimes, to make sure, we mow,water!! and wait a bit for the weeds to 'jump up'; and then apply the Roundup?
This strategy will work every time.