The rest of the sailing community here might think I'm an idiot, but I'll share with you my way of tuning a rig. I learned this on my first boat, a 23' trailer sailer. Since it was a trailer sailer, you had to take the mast
down each time and re-tune with every launch. Boy, did that get old.... Take it for what it's worth:
First, doing as you said is fine... grease stuff, look it over for rust, check for "fish hooks", or places where the cable on your shrouds me be failing. Look for rust coming out of the joints, etc... Check attachments points, etc... just do a nice, slow look-over for anything that doesn't seem right.
Next, get the mast into position (I think it already is on your boat).
Now, look at all of the shrouds. See where they attach to the mast and just make a mental note. Think thoughts like, "If I tighten my backstay, it will compress the mast, pull the mast aft by the top of the mast and give it a slight bow to aft." Just look at all the shrouds and understand what tightening and loosening them will do. This is more of a holistic approach than reading fancy rigging books
Next, my big secret: Lay down on the deck
forward of your mast with your feet pointing toward the bow and your head
touching the mast. Look up the mast and sight it like you would a piece of lumber
at the lumber
yard. You'll easily see any incorrect twists and bends in the mast that are a result of incorrect tuning.
Now, keep working your way around, using the knowledge you have of which shroud
does what as you tighten it to get all the twists and bends out. Just keep at it, never over-tightening, sometimes loosening, but achieving a nice, straight stick.
If you desire any aft rake or special tuning, you can do that fancy stuff this way too.
Tuning a rig is a lot more simple than the books
and riggers want you to know. It's just a matter of pulling "here and there" on the mast by tightening the turnbuckles that associate with the direction you want the mast to bend. Laying on the deck allows you to see the bends.
Last tip: If you want to get a good view of the fore/aft rake, get off the boat and go walk at 90 degrees or 270 degrees to your boat's bow. Walk far away and take a peek... then get back on deck, lay down and look at the mast from the front again.
Take your time and take as long as the job takes. Could take 10 mins, could take an hour. You just have to be "at one" with the boat for this one.