Jay J has some good ideas. I just priced some blown cellulose at R-19 at .15 per sq.ft. plus the blower rental. R-19 kraft-faced fiberglass batts came in at .40 per sq.ft. Depending upon where you are at, you may want to have a total of R-30 to R-38 in the attic along with a vapor barrier.
I don't know your house, either new or old with a plaster and lath ceiling but you do need a vapor barrier. Ceiling joists are usually made with 2x6's (5 1/2" nominal) which allows for R-19 to its top edge. I recently looked in an attic with blown insulation and no vapor barrier and evidently the moisture caused the blown insulation to cake and clump together where it sagged well below the joist top thereby losing a lot of its insulation value.
If you use blown, then get a roll of Poly and a staple gun and go thru the attic to staple the plastic down into all of the joist spaces before blowing it. I prefer to leave the blown for the walls that you can't get to any other way.
I prefer fiberglass batts and would put down R-19 faced insulation in the joist space and then put R-19 unfaced batts side by side and perpendicular to the joists. I've seen some houses where they put foot thick bat insulation between the joists and you have these places above the joists themselves with nothing. I don't think attic moisture affects fiberglass as bad plus it is not as messy if you want to go back and add lights, etc. although it can be itchy.
This can be an easy DIY project, just wear long sleeves and a mask to breath through. Like Jay said, make a drawing or take pictures of everything such as wiring and lights before covering it up. I tend to make drawings and take pictures but a while back I wanted to put in grab bars in a bathroom and it took me a month to find the drawings so I could note where I put the extra bracing in the wall so the moral is to hang them up in the attic.
Watch out and don't cover up non-IC rated lights and keep air paths open to soffit and other vents. You may also want to nail down some 1x12" for a walkway before the second layer of insulation.
If you are going to hire this out, then get at least 3 or more bids and think about the middle one as the best. Government always takes the low bidder and you probably know what they get for the money. Good luck.