Hello Sergiu - Congratulations on your purchase!
For the tenant that is leaving...
1. Be sure you get a copy from the seller of the 60 Day Notice of Termination. Be sure you know how/when it was posted, mailed or both. Just some way for you to prove timeliness if it becomes an issue.
2. Next, be sure you get a copy of the tenant's check-in sheet that she should have filled out when she took possession. This is proof of the condition then. Sometimes however, these are not filled out or a part of her file. When you do your walk through you should take a lot of pictures to establish at least what the condition was like then, in case it takes a turn for the worse.
3. Be sure that you get a full accounting of the security deposit from the seller and these funds should be transferred to you at closing as you will be responsible for accounting for the security deposit when the client moves out and will be obligated to return any monies due her or provide a written accounting within 31 days of the day she returns possession of the unit to you.
4. I find that tenants like to have a list of what is expected of them on move-out. I provide this both when the lease begins and again once notice has been given. Tenants want their security deposit back and if they turn the unit over to you, empty, clean, and free of damage (other than normal wear and tear), they have a reasonable expectation of getting it back.
For the tenant that you would like to have sign a new lease:
1. It depends what parts of the lease you want to change and also how long the tenant has lived there. If they have lived there less than one year, you can raise rent, and terminate the current lease with 30 days proper notice (posted) or, if mailed, you need to add 3 days. You can't just change the lease without proper notice.
2. If they have lived there more than a year, you need to provide 60 days proper notice to increase rent or terminate current lease
You should consult the Oregon statutes to determine what type of notice is required for the kinds of changes you want to make. If you want to increase their security deposit for instance, and they have lived there for more than a year, you need to provide proper notice and allow them 3 months worth of security deposit payments to reach the new number.
Remember, this is not legal advice and you should definitely familiarize yourself with the Oregon Statutes. Good luck with your new place!