An 8" has 4 times more light gathering power than a 4".
Reflectors generally give you the largest aperture for the lowest $.  Larger apertures mean (generally) better resolution on planets and better light gather power for faint deep sky objects like galaxies and nebulae.   However, reflectors require alignment of the mirror (known as collimation) which takes time to learn and frustrates some people.  Bigger reflectors like 8" and 10" Dobsonians, which can be purchased used at your price range, really do a great job on all objects.  Smaller reflectors like 5" and 6" reflectors do well on planets and some DSOs but don't show fainter DSOs as well as bigger 8" and 10".  The light gathering power of telescopes goes up with the square of the radius.  An 8" has 4 times more light gathering power than a 4".   There will be minor optical compromises with a Newtonian or Dobsonian reflector that are usually not visible to beginners except at really low magnifications (20X) (which we use a lot because some of the best DSOs are really big!).  These telescopes will perform adequately with low priced Plossl eyepieces but benefit from more costly eyepieces (which you can purchase later if you stick with the hobby).  Note that 8" and 10" telescopes are really big.  Like take the entire back seat of a car big!!!  They are also heavy!