Choosing a temporary structure looks like a size question and is really a site question. Work through it in this order and most of the decisions make themselves.
Start with the surface, not the span
Grass takes stakes, which is the strongest and cheapest anchoring there is. Hard standing cannot be staked, so the structure has to be ballasted, and ballast for a large span is heavier and more awkward than most people expect.
That single fact rules structures in and out before span is even discussed. A pole tent on tarmac is a bad idea; a frame marquee is designed for it.
Then pick the structure type
A frame marquee gives clear span with no centre poles, so the floor plan is not built around obstacles, and it works on any surface. A stretch tent has no fixed footprint and fits sites a rectangle cannot — walled gardens, slopes, courtyards with trees.
Camping tents are a village, not a structure, and are priced per unit. Inflatables win when pitch speed matters more than anything else: minutes with two people rather than a morning with four.
Decide what gets printed
Roof panels are the highest-impact print on any structure, and the most commonly skipped. If anyone will see the site from a grandstand, an upper floor or a drone, the roof is the only panel that reads.
Sidewalls are the cheapest large-format branding available and can be swapped between events. On stretch tents, keep print to the valance — artwork across a tensioned curve distorts and there is no clean way to pre-warp around it.
Specify the anchoring properly
Ask for the wind rating in writing, for both the staked and ballasted configurations, and ask what the de-rig threshold is. A supplier who cannot answer has not thought about it.
For ballast, get a figure per leg rather than a total, because that is what the crew actually has to carry. And remember the order of operations when it gets windy: drop the sidewalls first, because walls turn a frame into a sail, then strike the roof.
What to send when you ask for a quote
Span or capacity, the surface, how exposed the site is, how long it stands, and artwork. A photograph of the site is worth more than a paragraph describing it.
If you already own frames, send the make and the keder profile — reprinting panels is far cheaper than replacing structures.