You've asked this question multiple times in this thread, folks have answered but not directly...
To set posts in a straight line -
Figure out exact placement for first and last post (measure out from the house)
Set first and last post in line
Run a stringline from first to last on the outside edge,
Install all intermediate posts using the string line to keep them in line with each other
A stringline is much cheaper than a transit and is a better tool for the job.
Squaring up your structural framing -
use the 3,4,5 method only go with 6,8,10
Measure 6' along the house, measure 8' out your first joist (sight it to make sure the joist itself is straight), make sure the measurement between those two marks is 10'. You could also go with 9,12,15 since your deck is 14' wide.
When your structure is complete, cross measure to make sure it's square - take two diagonal measurements across your structure (from house on left to rim joist on right and vice versa) - they should be the same number. If they aren't, you need to scoot your structure until they are. Joists should not be fastened to the beam before this step! If your measurements are off by an inch, you need to move your structure 1/2" towards the larger number. Of course, this is assuming you can lump a 22' structure. At 5' high, you should be able to shoulder two joists in the center and push it to one side.
If I can offer some strong advice, make damn sure you know what you're doing with the hot tub deck structural framing. You might post your plans for framing the 10'x10' deck so we could help make sure your clients don't take a fall when they invite some friends over to go hot tubbing. I'm not trying to belittle you, just realize that a freestanding 10'x10' deck sitting 4'-6" high holding a few thousand pounds of water and people needs to be adequately built. As you're a remodeling guy getting into building decks, this project might be better built if it's engineered than winging it.
Mac
P.S. If you want to buy a transit, buy a transit. If you're trying to justify the purchase to wifey, this is not the project.