The cutting back would be enough to prevent flowering - there are no shrubs (that aren't effectively sterile variants) that don't flower when big or old enough. Flowers not having been seen on a particular example is not an automatic indication that a suggested identification is incorrect.

There's a few things to keep in mind. The tropical sun is stronger than where you are. Many tropical plants that are home grown outside of the tropics are understorey plants, that is they grow under the shade of other plants/trees. They like high humidity but even those that normally get direct sunlight will burn in it if humidity is too low. So that is the main issue, keeping humidity up. The types of soil you use depends on the types of plants you grow. There are plants that like acid soil conditions and others that prefer higher pH (alkalinity), with most of them being happy with neutral soil. Also, some will like it soggy, and others well drained. You need to find out what the particular plants you have prefer. Nutrient requirements are also variable. Generally those that are epiphytic or semi-epiphytic in origin have low nutrient requirements. But Amorphophallus and some others have high requirements. You can find this out as you get the plants. With a greenhouse you need to be careful it doesn't turn into a heat trap while you're away and cook the plants. You'll need to work that out in the planning.

I suggested lavender initially from the general impression but unless you have seen this plant up close I don’t think you can be 100% certain. At that distance it could possibly be a Salvia.

I did have spearmint in that pot years ago. that would grow tall and had bigger leaves. This one is crawling . It does smell minty! 😃