Here are some questions to ask when you buy original art:
Establishing a budget you are comfortable with is important of course and this will also help you to focus on artist's work you can afford. If you'd like a rough idea of how much to spend, I've heard people suggest spending half of one month's income over a one year period on one quality piece of original art.
Size, colour, tones (light and dark), textures, composition etc. are properties to consider for the art to work well within it's intended space.
This will help you clarify whether you would consider a 'one off', in a different style or if you'd rather stick to the artist's signature style.
An original artwork by the artist should be signed and will probably be dated, possibly titled as well.
A useful document proving ownership and authenticity. Not all galleries offer this though and some collectors simply rely on the artist's signature to show authenticity
If you buy online, it can be difficult to make a decision about a work of art you've never seen, so it makes sense to be able to see it with your own eyes at home and to be allowed to return it if it isn't as you expected.
It is worth checking beforehand as many galleries can charge extra for delivery. The larger the work is, the pricier delivery. So its something to factor in.