Hi Chantz - When you purchase a tenanted property you basically assume the lease agreements currently in place. You will want to read these carefully as they will govern until you can legally make the changes you are hoping to make. In Oregon, I would need to give at least 30 days notice of a rent increase on a month to month lease if the tenant had been there for less than a year. If they have lived there for a year and one day or more you must give at least 60 days. Washington may be different so make sure you read up on this and understand it before you do anything. In Oregon the notice requirements to terminate a month to month tenancy are similar to the above. If you are buying this property from your father, perhaps he would agree to post the rent increases now ow so you don't have to wait as long after you own the property.
I wholeheartedly agree with the other posters that say that if there is a tenant with a history of late payments, lease violations etc., choose that unit to live in if you must live in a unit. My concern for you is that you say you need the rents to increase by $150.00 (total? Per unit?) to be able to make the mortgage payments. Your costs on this tri-plex will include many expenses on top of the mortgage (taxes, insurance, any utilities you are responsible for, repairs, capital improvements, unit turnover etc.,). If you were hoping to pay these with your "some extra" after raising the rents and paying your mortgage, I think you might find yourself in trouble right out of the gate. You can read a lot about the "50% rule" here on BP, but it basically says that over time, your monthly expenses on a rental property will be about half of the total rents you collect. This does NOT include the cost of your debt service (mortgage payment) - that comes out of the remaining half.
If you have all that factored in and you are moving forward I would do some research on Craigslist and any other rental sights that are used in your area. Do a search with the number of beds/baths of your units and put in a ceiling rent that is the rent you hope to charge after the increase. Now look at the pics and area and amenities and compare them to yours because this is very likely what your tenants will do as soon as they receive the rent increase. If there aren't many units available below that price or they are not as nice as yours, your tenants will see this too. If there is a lot for rent at that price and they are nicer than your place, you will probably lose tenants. Vacancies really impact your bottom line but you also need to keep rents close to market or you lose that way too. The trick is to know your market so you know how much you can push rents without going too far. $150 below market is a lot!
If it were me I would immediately increase all the rents to the amount that the market told me was appropriate. I would give a 60 day notice even if I could legally give a 30 notice because with that kind of a raise I think it best practice to give them time to restructure their budget AND it gives them time to look around and learn that even at the new rent, they are getting a good deal. If you only give 30 days, many tenants have a knee jerk reaction and give their 30 days notice to you that they are moving. I have seen it happen where they do this and then look around for another apartment and realize too late that they were getting a good deal. Now you (hopefully) already have another tenant lined up and will incur the cost of a turnover that you could have avoided.
I would be hoping to keep all the good tenants at the new rate but I would be prepared to invest in a proper turnover if they left. If you don't have the funds to do what is necessary to attract new renters at the new rate (new carpet, fresh paint etc.,) you might have to play it a little different. You will have turnover costs and if you have to wait to do the work while you save the money the vacancy will kill the whole increase and then some... Another option would be to give a 60, 90, 120 day notice of rent increase where you are basically increasing it $50 each time but tell them about it all up front. This is irritating to renters but it might space out any attrition you get...
Good Luck!