Raising rent on inherited tenants. Advice needed ASAP!

[Rikako W.]

We are a few days from closing on our first deal! We'll be house-hacking a 2-family detached house in Union City, NJ, about 12 min bus ride from Manhattan Port Authority.  We are inheriting an existing tenant who is paying below-market rent.  They are on month-to-month lease and paying $1150/month.   After visiting other rentals in the area, I think market value is conservatively $1450, if not more.  It's 3 br, 1 bath, and has pretty generous living / dining area. Bathroom could use a renovation but otherwise it's in a pretty good condition. 

We are closing next week Oct 17, and in NJ we have to give 30 day notice to raise the rent. I have questions / concerns of how we should approach this. Which one of the following scenario is the best? Any advice is greatly appreciated!

Scenario 1:

After we close, let them know immediately that we are raising the rent to $1450 and give them the choice of signing a year lease. Most likely they will move out, and we have to find new tenants with a lease starting Dec 1.  (I don't know if it's hard to find qualified tenants in winter in Northern NJ? any inputs?)  We might take time to renovate the bathroom and rent it out starting Jan 1.  

Scenario 2: 

Offer a 6-month lease from Nov - April at something like $1200, and then raise it to $1450 (or more) next May. This way we will avoid having tenant turnover during holidays. This will also give us time to renovate the exterior siding, add laundry in the cellar (that tenant can use), and freshen the entry area.  

My concern is, if we sign a 6 month lease, and then a 1 yr lease with $250 increase, that is probably considered "unconscionable" according to NJ landlord-tenant law. 

Scenario 3:

just increase to $1200, and keep increasing by small amount ($50/yr) every year. We are limiting our income and obviously we want to avoid this. 

-----

The seller's 1-page lease is hand written and it's so illegible that I can't even read the date on the lease.  So I don't know how long the tenant has been there.  We've been trying to get clarification from the seller but we haven't had any success.  

We are super excited to close, but this tenant question is concerning us quite a bit. I would appreciate any suggestions. 

Thanks in advance!

Rikako