Some general thoughts, from someone with a longstanding relationship with a Lister B.
They are quite nice things to have and play with. I personally would get bored sitting watching it chuff away all day and at shows there does appear to be an expectation that this is what you will do. They come in a wide range of shapes and sizes - vertical, horizontal, open crank etc and everything from pick it up and carry it through to needing a specialist trailer to move it. The Lister D is a good introductory model, although personally I think it looks a bit boring. There was a very comprehensive 'how to' series on rebuilding them in Stationary Engine magazine in the late 1990s which is available through back-issues.
I would definitely start by taking out a subscription to Stationary Engine. It will give you a feel for what's out there and the classifieds are a good price guide (and might even contain something you like the look of). There are some good vintage auctions as a source of an engine too - you have just missed the most recent Cheffins one last weekend but worth a look at the results from, I think, Sale 4 as it will give a guide to what was around and how much it made. They also turn up at Newbury, at what used to be the Sodbury Sort-Out.
Alongside the engine, it's worth thinking about whether you have space for something for it to drive. Most drive off a pulley so you can adjust RPM to suit by varying the two pulley sizes. Pumps are popular but there are also stone crushers, sawbenches, reciprocating saws etc. depending on space and pocket.
Parts availability can be assumed to be very limited. Once rebuilt they do so few engine hours that you are unlikely to ever need any, but during the rebuild process you are likely to need to custom manufacture any parts needed. This means it helps to have something largely complete, fairly common, or have/have access to good engineering facilities, but if you enjoy such things, that restoration challenge for something rare is part of the fun. If you don't, buying an older restoration of something fairly common (Lister A, B, D or a Petter) and doing a strip, clean and re-paint would be an easier option.
The Lister B I referred to above dates from 1949 and is completely unrestored. My grandfather rented out his woodland to a pair of woodmen who bought the engine and an old Dennison sawbench and kept them in the woods to cut firewood. After the clean air act, the engine and bench were abandoned in the woods where they stayed until one day in the 1960s when my grandmother and mother had gone out shopping and my father turned up early to visit. He got roped in to helping extract the engine and bench which were dragged out behind my grandfather's Hillman Imp, and installed beside the garage as a fait accompli before my grandmother got back! My father then inherited the engine and bench, which technically now belong to my mother, but the only person who knows how to use them is me, so in time they will probably come my way, unless my mother does something mad like sell them to a scrap man (this is within the realms of possibility).
Alec