Deep space observing is a contest against faintness, and there are only two weapons: the aperture of the instrument and the darkness of the sky. Everything else, including magnification and cost, is secondary to those two.
Aperture, and what each step buys
Light grasp goes with the square of the diameter. Moving from 130mm to 200mm gathers nearly two and a half times as much light; from 200mm to 300mm, more than twice again. In practice that means a Messier object that is a faint smudge at 130mm shows structure at 200mm and detail at 300mm, on the same night from the same place.
The sky, which is usually the bigger factor
Moving from a suburban garden to a genuinely dark site typically gains more than doubling the aperture does. This is unwelcome advice because it involves driving rather than shopping, but it is the honest ranking: a modest instrument under dark skies beats a large one under streetlights on almost every faint target.
Why fast focal ratios suit this work
Deep sky objects are extended rather than point-like, and a fast instrument with a low power wide field eyepiece gives the brightest possible image of an extended object at a given aperture. That is why deep sky dobsonians are typically f/4 to f/6 and why the wide field eyepiece is the accessory that matters most here.
Questions people ask about telescope
What is the best telescope for deep space?
The largest aperture you will carry to a dark site. A 200mm to 300mm dobsonian is where most serious visual deep sky observing is done.
Can I see galaxies from a city?
A handful of the brightest, as faint smudges. The great majority of deep sky observing needs a sky darker than a town provides, whatever the aperture.
Do I need a goto mount for deep sky objects?
No, but finding faint targets by star hopping is a learned skill and a computerised mount removes the learning curve. Many observers use one and still learn the sky.