I will write a quick explanation guide on each type of display.
TN: TN panels have many benefits over popular CRT monitors: lower weight, lower cost to produce, lower power consumption, they’re much thinner, offer clearer pictures, have no realistically achievable resolution limits, offer flexibility in size and shape, and the ability to eliminate flicker. That being said, TN panels weren't and still aren’t perfect, and compared to the previously popular CRT monitors, they’ve suffered from limited viewing angles, uneven backlighting, worse motion blur, higher input lag, dead/stuck pixels, and poor display in sunlight.
IPS: IPS was created to address the shortcomings of TN panels. IPS panels seek to solve TN panels’ issues of poor colour reproduction and viewing angles. In this regard, IPS panels have largely succeeded. Not only do they offer a higher contrast ratio (superior blacks), high colour accuracy (which leads to IPS panels also generally looking less “washed out”), but IPS panels also have very little colour shift when changing the viewing angles. The tradeoff to this is that IPS panels have slower response times, higher production costs, higher power consumption, and lower possible refresh rates. IPS panels have traditionally been 60Hz, although, as with all monitors, they can be overclocked (results will vary). There have been improvements to IPS panels over the years, and slightly different revisions in the form of E-IPS and H-IPS, but ultimately the differences between these versions are inconsequential to gamers and those not involved in graphic design as a job.
VA: VA panels offer a solid medium between TN and IPS panels. VA was created to combine the advantages of IPS and TN panels, and largely did, although they did so with some compromise. That seems to be a theme in the world of monitors.
Compared to IPS panels, VA panels have the advantage of higher possible refresh rates. Although most are currently 60Hz, there are a few that are above 60Hz. VA has more advantages over TN panels than IPS, with better colour reproduction, higher maximum brightness, and better viewing angles. VA panels do have the best contrast ratios of all panel types mentioned, but they also have the worst response times of the monitor technologies covered here. This causes blurring in fast-moving pictures and is disadvantageous to gaming.
I would pick IPS as the "low refresh rates" is no longer a valid argument (Some monitors have 144Hz refresh rate and IPS panels). About us helping your getting a new monitor, I need to know your primary interests in the monitor and your budget. (For example, is it for gaming, editing etc and how much money are you willing to spend on a single monitor?)