Lots of good suggestions above. A few more thoughts...
Since the OP wants to glue to a vertical surface (and assuming that the item can't be laid on its side while the glue dries), quick tack/setup is important.
Contact cement works great, but the fumes are powerful and you only get one shot at alignment.
The amount of stress on the application should be considered. We can often get away with using an adhesive that isn't particularly strong because there won't be a lot of force applied to the finished product (securing trees to a hillside, for example).
In this hobby, we often use plain old white glue in ways that it wasn't really intended for, and it's very benign. Although it's not designed to work on non-porous surfaces, it can be used to hold plastic or metal scenic items in place, for example.
It can be a challenge to find adhesives in an economical size - a small container often costs almost as much as buying 2 to 4 times as much, but the remainder will go bad before it can be used.
