I personally use the Wisconsin Realtors Association Lease and then have my non-standard rental provisions and additional rules, lead disclosure, etc. I do use the Pet Agreement from BP forms. I would say it's not worth spending the money on the attorney, but that may depend on whether your county is more pro landlord or pro tenant. As far as the tenant paying the 3rd week due to disability, that sounds like hogwash. Social Security checks are paid on the 3rd, not the 3rd week. I have made due dates on the 3rd for people in that situation in the past. I also let a tenant move their due date to the 10th, but made them pay up front for those 10 days before I changed it. I would be very careful with the lienency you give the tenant. I believe we condition tenants, to prevent them from walking all over us. Also, if you closed in the middle of the month, you should have received prorated rents at closing. I would also ask her for proof of her disability payment showing the date it is paid.
As far as the banking, I would recommend creating a separate checking account for the property. You should be able to use a personal account with no fees. If your current bank doesn't have free checking, go to a different bank. I don't recommend mingling the funds with your personal account. It's a business, so treat it as one. I like Quickbooks for bookkeeping, but I used a spread sheet when I bought my first property. No sense in spending the $150 until you have more info to track.