When buying a grade horse you should get a bill of sale for sure.
Also write the basic info on the memo line of the check and you should if you use one for a paper trail.
Cash is usually not the way to buy a horse even if it is from a close person.
They can turn on you, and then you have to prove that you bought it.
So use the proper paperwork
for your purchase.
The best thing is to pay by check but preferably money order or certified bank check and have a proper bill of sale for the horse (download and print here).
Be sure that the person selling the horse actually owns the horse.
Selling a horse that isn't yours is an old trick that goes back many, many years. So beware.
On the bill of sale have the sex, age, color(s), and any marks on the horse such as a brand or a scar etc. If you buy or sell a horse that has any problems such as navicular or can not be spurred it should be on the bill of sale.
Also have the name, address, phone number, and email of the seller and the location from which you bought the horse on the bill of sale.
Have any kind of copy of the "Horse for sale" ad as an extra clipped on your attachment to the bill of sale for safekeeping.
Be sure that the buyer and the seller both sign the each of the same copies of the bill of sale. Family and friends often end up in a court case against each other so how you feel about them now isn't as important as having proper paperwork.
Horse sales are generally considered to be sold "As Is" so buyer beware.
There are grounds for fraud such as the seller telling the buyer that the horse if great with children but the horse actually bolts when a child is on it's back.
That gets to be hard to prove so check the horse out very carefully before you buy it.
When you are buying a horse and you have little experience you might consider asking a friend who is well aware of the dos and don'ts of buying a horse to accompany you to offer advice.
You should ride it and test it thoroughly. You might also have another person ride it as well.