I am buying a mobile home that has a three-quarter inch particle board subfloor. I plan to patch any holes and then overlay the particle board throughout the entire trailer with either plywood or OSB. Given that the new floor will be resting on the existing particle board, what thickness do I need and should I go with plywood or OSB? Don't want to be too cheap but I don't want to overspend either.
If you do in fact have only the 3/4" particle board now, you should not consider it structural. Therefore, I'd use 3/4" (23/32) tongue-and-groove OSB, which is standard as a basic single-layer subfloor in new homes. In areas where you want to install vinyl or other flooring requiring a prepared surface, use 3/4" t&g BC plywood to avoid the need for additional underlayment.
If you actually have MDF (or some other high-performance pressed-particle product), which has more structural integrity, I'd consider a 1/2" or 5/8" BC, with the joints staggered from those of the MDF. You won't save a ton over the OSB (it may actually cost more), but it'll result in less of a height difference and has a nicer finished surface.
First I am glad to hear you say overlay the existing subfloor. The main reason I say this is that the subfloor usually ends up under the wall framing and trying to remove or replace it can only be done by cutting and rematching the height.
As far as what to place over the existing has two items to keep in mind.
The first is if you use too thick of board your walls bottom plate gets the amount of exposed wood available for access reduced. If you plan any open wall work such as replacement of a wall with sheetrock you can loose to much of the plate to nail to. So try to keep at a 1/2 inch maximum.
The other part of selection of material will depend on what you are finishing the room in and type of room. If your existing floor is in fair shape both plywood and OSB staple or screw down nicely for living rooms, bedrooms, and halls. I prefer a exterior grade plywood with one side sanded(up) but have also used the OSB. If your in a bathroom or kitchen area hardybacker or cement board is the better choice.
Basically installing this subfloor is the same concept as installing a subfloor on a concrete slab with exception of anchoring methods.