Well, if you want better sound quality then go wired. If you want clsed backs for home, gaming and to be successfuly used with an entry level dac/amp then take a look at the dt770/32 ohm which is cheap and really good. If you want same ok priced allrounder for home and gaming also, you can take a look at an dt990pro/250 ohm. For that you need a better amp, though. For cheapper and somewhat portable open back you can also check the yamaha hph200, though the build is on the plastiky side but the sound superb. For in ear high quality at a fantastic price you can check the meze 11 neo. You can't go wrong with those.
I recommended those for a starter, as I know them all and they are very good price/quality. For portable allrounder and hifi music from phone go for the 11neo, for home use gaming, dt990, for office isolation dt770, for portable openback allrounder the hph200 or something like that. They all are in $60-150 range so, ok for a starter. Sound quality wise they are all very good. So hope that helps. First you need to find out how you will use them mostly then chose your first :)