I might second the EB2S recommendation, though it is a crap-shoot as to whether you get the ones that sound as intended or not. I think that it has been accepted that these are not consistent on how they sound coming from NiceHCK. Still, if you get the good ones, they are a very solid budget choice even at their full price.
Having said that, another recommendation of a budget bud with a mic would be the new FiiO FF1. They aren't perfect, but they have a mic, with detachable cable, and have more of a full rounded sound (as opposed to the EB2S which are good, but much thinner in sound). They have big bass quantity, and have clear treble without the added 3K boost so common on budget sets (heck, on most sets coming out nowadays). In other words, they don't seem to have any offensive tuning (to my ears). These really sound their best coming from non-audiophile sources (from my experience) such as a phone, or PS4 in your case.
Another potential recommendation might be the
LUN SHENG AEOLIAN Bells. These can be either with mic or not, because they don't come with a cable. You will have to provide your own. They have a very addictive sound to them. They aren't perfect, and have a bit thinner sound to them compared to the FF1, but nothing offensive that hurts the ears (for me anyhow). I also rather enjoy the fitment of these, and can listen to them all day without discomfort, nor worrying about them falling out. The good news is that they are built like a tank, and you could probably actually run them over with a tank and they would be fine. Also, because the cable is detachable (MMCX), you can always replace the cable if it ever gets damaged.
The bad part of these though, is that QC on these is not so good. While others on here have gotten sets that are great right out of the box, I have had issues with 2 sets. The first set had a blown driver on one side (it worked but output massive distortion with ANY sort of volume past really low level). The second set has (I'm guessing) an impedance mismatch, because one side is quite a bit louder than the other (the volume balance has to be at about 40% to make them sound even). If you can live with the fact that they have some QC issues, these actually sound pretty good for a budget set.
P.S. You CAN choose (for $20) to have the A-Bells come with an MMCX BT cable as well; however, I opted out of that one, so I cannot tell you how good/bad it might be.
I don't think I would recommend the AKG line for
@WoodyLuvr; specifically the K702. I could be totally wrong here, but over the years I have gotten to know him a bit, and while I LOVE the K702, and they are among my favorites, they are very bright. I think that normally he looks for something that is not so hot in the upper regions (more laid back) and warmer overall. These are neither of those things... they are pure analytical/studio.
These are notoriously harder to drive than people have ever given them credit for because they are not very sensitive and have mid impedance while only having SE capabilities. They can undergo surgery to make them balanced, but at stock level, they aren't wired at the drivers to be balanced.
- 62Ohm impedance
- 105dB/1VRMS (not to be confused with 1mW, which these would actually be 92.9dB/1mW making them fairly insensitive and harder to drive from contemporary 3.5mm ports, except those desktop amps that have the capability of higher number from the same)
Either way though, all some really good recommendations.