New Lease Agreement after initial lease expired

[Jonathan Pantages]

We are newbies, so bear with us...

In 2018 we moved out of our home in California  We rented our house and signed a one year lease with our renters for $1300 a month.  The year contract was up in February of 2019, but due to some health issues (mine), and the renter trying to buy their own home, time passed by and now a full year and 3 months or so has gone by.  We did not increase the rent. 

I want to give them another one year lease agreement that goes into effect on July 1.  If I send the notice tomorrow 5/31, can this go into effect on July 1 or do I need to give them 60 days?  

My understanding is when the initial agreement expired, the "contract" technically went month to month.  Do I need to send notice terminating the month to month and introduce the new agreement or just send the new agreement?

We gave them a good break on rent and never increased it, so does a $100 increase feel unreasonable?  Other similar properties are going for $1500-$1600.

For what it is worth, they have been slightly late 50% of the time, but have paid late fees, communicated well and never did not pay.  They do complain a lot about trivial, cosmetic items, but the tenant is wanting items done that really are a personal preference, not health and safety issues.  For example, she wants the kitchen floor replaced because she doesn't like the design...The floor is in fine condition, she just doesn't like it! 

They have stated that they do not want a long term contract, so they could leave, but there are people who have inquired about renting the house and we know we could increase our rent significantly if they choose to leave and we get new tenants.  

Thanks so much and let me know if you need additional info to answer...Feel free to drop me links to articles that may help me with this. 

JP