Second hand engine

First you need the same exact engine, a 1.9 TD to guaranty that it will fit perfectly but you can even install the S16 engine, but you will need new pretty much everything.

Check if the engine is uncontaminated. I don't know if that's what you call it in the US, but here we call that to an engine that is dry - no oil stains, no water marks, has no sealant products anywhere and is clean on the outside.

A good engine should not have rust anywhere, check if everything is in place, like if the parts don't move, has no damage at all. Obviously you will find some rust, for example on the clutch pressure plate, but you shouldn't find excessive rust.

Also, before you ask for an engine, try to find out how they treat the engines. An engine should always be tested before it is uncontaminated, try to find out how the whole process works and if they checked the seals of the car. When you ask for the engine, try to find out what kind of person had the car with that engine and how many miles it has. Usually older people take better care of their cars and usually don't push the car too much. If the company selling you the engine actually knows the person, the better, for example, if the older owner is friends with someone on the company, the more you know about the driving habits the person who used the engine the better.

Also, try to get a warranty for that engine, for at least 3 months, never less than that because some engines were very poorly treated over time and that gives you time to see if the engine is good.

But in the other hand: is it really worthy repairing that car? What I am saying is, if you have money to buy and replace the engine + money to repair it in case it's in a bad shape, go for it, otherwise you should think twice.

* this is by experience on buying an engine, I am not mechanic, I am far from being one.

Steve W, that is true, but in this case I think he will be good. Peugeot 306 engine is mechanical, has nothing electrically controlled at all compared to other engines of the time.
There may be small differences, like supports that hold the parts or something, but he can go take them on the old engine, I don't think that there will be any difference on engine construction, as long as the new engine is also a 1.9TD.