This will likely be a location specific issue, so it doesn't hurt to check your local codes.
All the fire rated work that I've done has been between units (both to other units and common areas) and any load bearing structures of a multi-unit dwelling. When we do that, fire blocking is installed in the ceiling space as well to prevent a fire from traveling through the ceiling to another unit. For everything else within a single unit, and in a single family home, we don't use any fire rated drywall.
Edit: A few reasons I'd disagree with Eric on this one. First, I'm presuming you already have a certificate of occupancy (or someone did) to move in with an unfinished utility room. That required an inspection that presumably allowed the space as is. Next, most codes for combustion devices (furnace, gas hot water) require that you have ventilation. Installing a vented door is perfectly acceptable and won't provide any fire stopping. And, finally, most HVAC's (if the furnace is forced air) will be connected to vents that run to every room in the house. From the little I saw, the furnaces and utility rooms in searches likely referred to multi-unit dwellings, and that does need to be fire stopped. You also have to use fire caulk around every hole. Our multi-unit buildings also have sprinklers throughout and spring loaded vents that snap closed in event of a fire.
That all being said, there's absolutely nothing bad about installing fire rated material around the furnace, other than the extra cost and that it's a bit more difficult to cut. If you want to do it, then by all means, do so.
Edit 2: One last note, realize that fire rated drywall increases the resistance from 30 minutes that you'd typically see with 1/2" drywall to 1 hour. Fire rated doesn't mean fire proof.
Option 3 is the sanest IMHO. You can get a bucket of drywall mud for $15 and do a "skim coat" over the panels to create a flat surface. No need to sand first; this stuff will stick to anything! Once the mud is dry, you can sand it to get a smooth look, or texture it. Texturing can be done with cans of spray-on texture you get at big box stores, or using a texture sprayer gun. A pro will be able to do the texture part much better than a novice, so if you want a textured wall, I recommend hiring that part out for $100 or so. With the right equipment and an operator of moderate skill, it's a 30 minute job. If you've already got an air compressor, you can have a go yourself with a sprayer attachment that has a hopper.
But whatever you do, match the texture or lack thereof to any drywall that abuts the paneled wall. Nothing screams "I used to be wood paneling!!!!!" like strange, awkward texture on a few walls that, upon further investigation, have more give to them when pushed on.
This is the approach I took on my wood paneled walls and today you'd never know the difference.
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The cost of prefinished wall paneling can vary wildly. Cheap 3/16 inch fake wood or patterned panels can cost around $10 per panel. A decent real wood veneer can soar to $40 each.
It is common practice to put paneling over drywall. Two main reasons for that are fire rating and ability to spread adhesive evenly so panels don't bulge between studs. There is no real R-value advantage. If anything, if paneling is not installed over drywall, the seams can be a source of air infiltration, negating any insulation value.
As a comparison, my drywall subcontractor charges me an average of $45 per sheet for 12 X 4 foot 1/2 inch rock, hung, taped, mudded, and sanded paint ready. This is really competitive with decent quality paneling, especially if you figure in a drywall untaped backer. If you do decide to go with prefinished panels, be sure you really like it, because you're gonna be looking at it for a long time! LOL