Many third-party monitors have DisplayPort inputs. Mini DisplayPort to DisplayPort cables are cheap and reliable, as they are simple pin-to-pin cables with no active signal conversion involved.
In the event that you want to connect a HDMI monitor, I don't know if. a passive Mini DisplayPort to HDMI adapter would work, or if you would need to look for an active one.
Typical choices include:
- 24" monitors with a resolution of 1920x1080 pixels
- 24" monitors with a resolution of 1920x1200 pixels – less common
- 27" monitors with a resolution of 2560x1440 pixels
Your Mac is too old to support 4K monitors or 4K TV sets, at least at full resolution. If color accuracy matters to you, look for a monitor with an IPS panel and 100% or near-100% coverage of sRGB (standard gamut).