Sounds like you own a piece of property with a home on it, and you want to buy the lot next to yours so you have a larger plot of land, correct?
If you've already established reasonable market value, and your confident in that number (that's a big question mark), then you and the seller can negotiate anything that makes financial sense to the two of you. But, separate market value from the payment terms, otherwise you have no idea what you just paid for.
Again, if you are confident in the market value of the property, then it's just a matter of determining the details of the loan. Interest rate, payment type, payoff date or balloon date, down payment, etc.
But be careful, don't attempt to write up the loan document unless you're an attorney, and preferably a real estate attorney. If you need an attorney, there are several good ones in town that are reasonably priced. One wrong comma, or word, and you could end up on the short end of the stick without the land you thought you bought, and without the money you paid the seller. Some people go find a "proforma" loan agreement. With that you get "proforma" legal help, which means you get nothing and cannot defend the fact that you relied on some source you have no idea about to create your agreement.
Note, as you may already have determined, the value of that land, being near water, has many factors that affect it's value, more so than a typical lot. And it's worth a lot more to someone else if it touches the water or has ownership into the water, if it has road access, if it has an elevation that can be built on, if it permits septic or has sewer, if it allows a boat dock, if it has views, etc.
If you do buy the lot, consider "joining" the lots for tax purposes, you'll pay less tax by doing so.
Use the same attorney to draw up the title documents (deed), and to issue title insurance. Without title insurance, and without doing a title search, again, you're in a position of potentially thinking you bought something the seller had the right to sell, when they may not actually have that right. Even if they show you a deed with their name on it, that doesn't prove they have the right to sell it.
Best of luck,
Broker | Partner | Keller Williams