First, determine what the rendered image will be used for.

On-screen viewing (web etc.): anything larger than 1800 x 1200 or thereabouts is probably overkill.

Offset Litho: determine the physical dimensions at which it will be printed (e.g. a half page, 6" x 8") and multiply those dimesions by the required pixels per inch - usually 300ppi. For our example, that would require a render of 1800 pixels x 2400 pixels. (Your "2000 res" render would be fine, as long as you mean that you're rendering to 2000 pixels.)

Large format inkjet: again, determine the physical dimensions at which it will be printed and the required pixels per inch. This is, emphatically, not the same thing as the printer's resolution expressed in dots (not pixels) per inch. So if you're given a figure like 720, 1200, 1440 or more dots per inch whoever you got it from has no idea what they're doing. For the absolutely finest quality you'll seldom need more than 240ppi. For display / exhibition graphics, you'll get away with 120ppi or even less.

Let's say you need to render to produce a huge poster, 5ft x 8ft. That's 60" x 96". If you render to provide a resolution of 100ppi at the final size, you need 6000px x 9600px. A big render, but not too crazy.

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