As background, one of my businesses is a professional cleaning service, although we don’t currently do construction cleans. Too much work for too little money.
Rabid Child correctly said you should clean from top to bottom. We also clean from left to right. This is important so that you don’t reclean parts that were already cleaned, either because you made them dirty again or because you got lost and had to start over.
Papertowels, even the best ones, will also leave a lot of lint. Don’t even bother with paper towels for house cleaning. Once you get the paint and stickers off of the windows then clean them once with a cloth and a second time with a squeegee if you want them really clean. Most cloths will leave lint. You can alleviate this, but it takes work. On my last visit to Sam’s Club I found some nice and very well priced cleaning cloths (get the natural colored ones, not red). Then let them soak in water and A LOT of bleach for several hours. You’ll probably have to wash them several times to “de-lint” them. A different tack is to use blue surgical cloth to clean windows, this is a fine weave that doesn’t have lint. Surgical cloth is expensive, but you can buy used surgical cloth. Some of that is not useable but it’s cheaper than the new stuff.
Definitely use a good shop vac instead of a regular vac, particularly for the first pass at vacuuming. Keep your vacuums clean and well maintained. Also, I hear great things about the new Mr. Clean Erasers but I’ve not used them yet.
For the tubs use a good degreaser and then use a window cleaner to shine them after. If you don’t follow up with a second cleaner the degreaser will leave the tub surface tacky. Since your father-in-law is the contractor you should work with him to try and minimize the dirt and stuff that his crews tramp through the house. Look for innovative ways to stop the dirt from happening and you’ll make more money more easily (fewer hours and less effort for the same money).
Also, and this is not the first thing most people think of, make sure you really take a lot of precautions to work safely. It’s easy to get hurt working on a construction site, even if the home is pretty much finished. Learn the proper way to use a ladder, razor blade, etc. Always look before you touch anything. You or your FIL should have some decent insurance to cover you in case of an injury.