115hp and four people, it has to be tiny somewhere. Tiny range, or tiny utility, or tiny seating/cockpit. Or it has tiny wings and needs lots of runway, there is no free lunch.
I don't believe a 914 weighs 150lbs installed anymore than I believe any of the other engine weights are installed weights, listed weight of engines is so ambiguous, some include this in the weight and others include that in the weight it is a lot of smoke and mirrors. It is predicated by the multitude of differences in individual installations. It is difficult to sort out the truth until you are way financially committed without investing a lot of effort in education and/or making trustworthy knowledgeable friends.
It is the total weight, and the frontal area of the installation one to another that matters. Oh yes and the hp and specific fuel consumption (sfc) best for my purpose's stated in lbs per hp hour but becoming more common in grams per kw hour.
Cheaper has different meanings to different people. Some would consider it cheap if they have to take out the front seat and sit in the back so they can stretch out there legs. I am not saying that would literally happen but you get the idea.
So some people are suggesting a Lycoming or Continental but I think the undertone between the lines is that they are not certified engines(to save money). You can obtain an engine without logbooks (which make it worth anything) for less money, my concern would be that I do not want stolen property, it can be missing it's logbooks for any number of reasons but that is the first concern I would want answered.
The D-motor interests me they have a 120hp or there abouts, I do not know how many engines they have sold or there record in service. But low moving parts count, liquid cooling and fuel injection with low sfc.
A Cessna 172 is a good airplane to compare to. 4 seats, 150hp more or less depending on year and modifications, 120mph, and as far as I am aware still the most produced light plane. It provided affordable entry to flying for many decades. Or a Piper Cherokee 140 or a 160 very durable little 4 seater with similar performance to the Cessna.
You would be hard placed to do better than a well cared for Cessna 182 or a Cherokee Charger 235 they have good utility.
I'm a multi fan, even a twin with poor single engine performance has better performance than a single with engine power loss. It's your family.