I stumbled across this by chance, and found the discussion interesting.
I lift four days per week, all compound, and it is based around squats, deadlifts, press, bench. I also row every day, following a 2k sprint training regime. As many have indicated, doing compound lifts is a time-proven formula for muscle and strength gain. And my own personal experience has been that rowing and strength training are complimentary to each other.
As to what order....well I fit it around my daily schedule, but usually lift in the mornings, row later.
However, my point.. I found it interesting that many want to loose weight, however this is often confused with wanting to loose body fat.
I weigh in at around 100kg, and as long as I maintain a lean body mass weight is the last thing I worry about.
Good luck out there..and enjoy it!
Baz