Have under contract a vacant lot where I will have a small house and a "granny cottage" behind.

By doing so, you are inviting a visit to court where you must prove that you are not doing a Land Contract (and you will lose). 

We are in a contract to sell a two family in North Jersey and should free up about $525k for a 1031.

Each state has different contract laws so you have to use one that is legal in your state. 

One way or another you are going to pay for your "tuition" - either a. being scammed by gurus hoping they will teach you the "secrets" on how to become a millionaire in your first year/month/property/flip/deal, or b. while doing mistakes in your first projects/deals (but at least you get something out of it and is the best form of education)  or c. putting a lot of time, effort and resources in learning about real estate investing industry (and that includes marketing, financing, negotiation, contracting/legal, taxation, hiring, project/people/property management, etc.).

-What type of contract should I use to write up the terms?

What is the right way to do this so that the contract is with me and not the previous owners?

We recently had a hard money lender back out of a land purchase deal we had under contract a week before closing date. 

I've pretty much stopped looking in PBC, in fact I'm actually under contract to sell one of my PBC properties and plan to look out of state with those funds.

However, repairs or improvements must be permanently affixed and add value to the real property.Costs and Escrow Accounts The costs of the renovations will be based on the plans and specifications for the work and on the Construction contract for all of the work requested by the borrower.