Those 90s games actually look great on a TV.
If you are wanting to emulate 100% arcade resolution, feel, ambiance, etc. then you want to use an arcade monitor. It may prove more expensive and time consuming if you go this route though. You can get a suitable TV new for $200 to $300, but you can easily spend twice that for a new monitor of equal size.
If it is 90s games that you are mainly concerned with, using a TV will be tons easier, and the games will look great anyway.
If you have money and time to play around with, a good hi res multisync monitor will prove more versatile, especially if you want to go back and play classic or vector games.
When comparing TVs to arcade monitors, many people will tell you it is a matter of opinion, taste, money, etc. and I agree. I have experimented a lot with both TVs and arcade monitors, and there are some differences in the way the games look.
But again, if it is 90s games you are after, there is no need to spend twice as much for a display. The games will not look "twice" as good on an arcade monitor. They will only look "slightly" different.