IMO, paneling should be removed and wallboard be put up instead. If you're doing this in a high humidity room, such as a bathroom, use the proper wallboard. (Traditional drywall is NOT to be used.)
Also, use a 1 cup to 1 gallon mixture of vinigar to water, respectively. Don't use the bathroom for a couple days and then clean the walls. When you're finished cleaning, or are ready to paint, make sure you PRIME/SEAL the walls with a good primer/sealer such as Latex Stain Kilz. Put on 2 coats of it. Then paint with a high-quality paint that's used in high-humidity rooms. This type of paint has Mildewcide already in it. (DOn't use the paint where you add it to the can yourself.) Buy your paint supplies from a Paint Retailer like Sherwin-Williams, Finneran & Haley, and so on. THey're listed in the Yellow Pages under PAINT - RETAIL.
My best to ya and hope this helps.
PS: It may be a rented home now but if you decide to sell it later on, you may lose value. Plez do the job right. If you have to, up the rent to keep out the rif-raf. WHen someone wants to know why the rent is so much, show them the Labor & Material's Bill!