In the process of finishing my basement and one of the rooms has mechanicals on the ceiling. Because these mechanicals cover ~40% of the ceiling I want to frame and drywall the entire ceiling at the same height as opposed to a box around the mechanicals. The lowest point of the mechanicals 8' 3 1/2" Hoping to have an 8' finished ceiling height. What type/dimension wood should i use to frame the ceiling? How should it be fastened to the I-Joists above?
I like the look of a drywall basement, and if thats what you want to do, then don't let others convince you a drop ceiling is better, do whatever you prefer.
In your scenario, I would build a bunch of "soffit ladders" and run them perpendicular to your floor joists.
You should use 5/8 drywall. I would put just one layer. 2 layers is unnecessary unless you have a permit and the building inspector requires it. You can then space the ladders at a max of 24" on center, 16" if you wanted to over do it. Normal 2x4s will be fine.
If you run into a pipe or any obstruction, just stop the ladder before and continue it after or build the ladder around the pipe and have it run through the ladder.
As long as all edges of the drywall can be secured and you can fasten every 24 inches within the drywall, you will be fine.
In the below picture you can see the vertical soffit ladder, I wouldn't worry about running 2x4s between the ladders, unless the ductwork prevents you from putting a ladder on the 24" mark.
If you have AC, I'd recommend putting insulation around the ductwork to prevent condensation from building and dripping onto the drywall, same with any cold water pipes. Insulation in the entire ceiling is also a good idea just for sound reduction.
Your concerns are:
Load bearing capacity of secondary joists
Sufficiently small joist spacing to prevent bowing of ceiling panels
Run 2x6 on edge as secondary ceiling joists, at 16"OC, if you have sufficient clearance from the bottom of the 2x6 to the floor. Otherwise use 2x4 with smaller spacing, e.g. 12" OC.
Plan out your lighting and the joists together, so they don't interfere. Also consider what size drywall panels you'd use, 8' vs 10', and what the best orientation is for the dimension of your space. Make sure you have joist running at the planned seams, and 16"OC in between.
You can attach point loads to the bottom flange of an I-joist. For instance, Weyerhauser specifies a load of 500lbs every 5ft. This is for a static load, which is the case for suspended ceiling. (For dynamic loads and loads that move, e.g. punching bags, it is recommended to apply blocking, engage the joist's web and install a brace to span two joists)
Attach joists to I-beam via 2x4 or 2x6 vertical stubs. Attach stubs to the bottom flange of the I joist. Attach joist to side or bottom of stubs. Careful here: you need to calculate the load per stub and thus the sheer strength or pull-out strength required of the fastener. The larger 2x6 stub will provide more room for more fasteners. Should toe-nailing or tow-screwing to the bottom be problematic, you could install blocking that engages the web and rests on the bottom flange, and attach the stub sideways into the blocking.
Once we know your preference for the type of ceiling and its dead-load, and the number of stubs and the span, we can help you calculate the requirements for the fastener (construction screws, nails or rated framing screws)
Use a laser level mounted high up just skimming under the most protruding HVAC/Plumbing to measure your stub lengths from the joist. They are likely all the same, but this is an easy way to verify the lowest point. Then when you mount 2x6 joists flush with bottom of stub you'll know the ceiling framing is level. Running secondary ceiling joists parallel or perpendicular to primary floor joist does not matter. Usually you'd pick the shortest span and consider your panel orientation.
For soundproofing and reduction of foot drop noise, use stubs sparsely. This will decouple the primary floor joist from the secondary ceiling joist. You can span 14' (I believe) of 2x6 for a double-drywall ceiling. This applies if you can hang the joist from a stud or post. Otherwise, if hanging from the existing joists, the manufacturer's point load limit applies which will dictate the spacing.
Apply double 5/8 drywall panel, glued together and jointly screwed to joist, if budget allows. Fill joist space with 1 layer of rock wool to absorb voice sounds and plumbing/hvac flow sounds.
Best also to glue strips of drywall to underside of subfloor, but this a lot of work with questionable performance if a lot of the subfloor underside is inaccessible due to plumbing/hvac.
Where required to span a larger section of HVAC plenum between secondary joists, shorten the stubs and budget for 1/2" plywood to which the drywall can be attached. Best to raise the joist too and attach plywood to bottom of joists, making the bottom of the plywood flush with all other joists.
For smaller sections of support in tight spaces around hvac, you can also use metal corner beads attached to the wall. The corner bead is then uses in an unusual manner, by attaching one lip to the wall, corner side down, and screwing the drywall to its other lip.
Drywall grid system
Alternatively, run a drywall grid system, which is a suspended ceiling for drywall panels, often used in commercial spaces. I have no experience with installing one, so I'll let someone else comment on that. You'd have to consider the achievable span of the main metal beams, the allowable deadweight, and how the plumbing/hvac mechanicals interfere with the grid, considering your limited -and not unusual- clearance.