Proper Underwear

Proper underwear can get a great therapeutic cool for both pain relief and long-term healing.
Breathes Well: Pretty self-explanatory, but critically important. If the underwear breathes well, it’s good. If not, then don’t wear it. Both fabric type and thickness matter. I have read that cotton transfers heat best, but that’s not true from my personal experience. I prefer polyester type fabrics and fabric that are both thin and designed to transfer heat like Nike’s Dryfit, Adidas’ Climacool boxer briefs. But, it is okay if you find any other fabric type that also breathes well.
Remember how I said to feel your testicles a few times a day? Well, that’s how you know if your underwear breathes well. If your testicles are hot, then it does not breathe well. Your testicles should be at their normal temperature throughout the day.
Provides Scrotal Support: Light scrotal support can help reduce scrotal sag and reduce blood pooling. This is helpful in the long-run for minimizing symptoms and improving healing. Light scrotal support means that the fabric gently supports your testicles.
Note that if you have to choose between breathable underwear and underwear that provides support, I recommend the breathable underwear.
Also note that a little additional support can be helpful for strenuous activities (e.g. heavy lifting, weight lifting, basketball, martial arts, etc.)

Improper Underwear

Improper underwear can cause aches, pains, infertility, and worsen varicocele severity. I cannot emphasize how much of a difference the underwear you wear makes on your symptoms.
Overheats Testicles: Overheating the testicles increases blood pooling, causes aches and pains, halts sperm production, destroys testosterone levels, and increases varicocele severity. I don’t mean to sound overly dramatic, but testicular hyperthermia is very underrated. Avoid underwear with thick or excess fabric, and that traps heat. Again, you will have to touch your testicles and check several times throughout the day to see if your underwear overheats your testicles or not.
Too Tight Around Scrotum: Underwear that is tight around the scrotum physically irritates the testicles, prevents testicular self-thermoregulation by physically stopping them from dropping down to cool (cremaster reflex), and tends to over-heat the testicles more often. Typically negative symptoms show within a few hours of wearing underwear that’s too tight around the scrotum. Go for light support, not compression.
Too Tight Around the Waist: Same as wearing tight pants or a tight belt, underwear that is too tight around your waist increases intra-abdominal pressure and makes it more difficult for blood to circulate. It is highly recommended to get better fitted underwear.

Underwear Types

Going Commando: If your underwear is causing you bad symptoms, I recommend going commando (without any underwear), until you get better underwear. Going commando helps keep your testicles cool, but, provides no support.
Wet Underwear: Making your underwear wet with some water is a great way of enhancing their thermo-conductivity. This is a great tip/trick when going to the gym, for a run or bike ride, and during any other physical activity.
Boxers: Boxers are typically better for heat transfer, however, they provide no support.
Boxer Briefs: Boxer briefs are better for support, however, they typically trap heat. Some boxer briefs are too tight around the scrotum.
Jockstraps: Jockstraps typically provide good scrotal support, however at times they can be too tight. Thinner jockstraps allow better testicular thermo-regulation.
Fertility Underwear: Fertility underwear is probably your best bet for getting all of the good and none of the bad out of your underwear. Fertility underwear typically have good thermo-conductivity, and some provide good support. However, they typically come at a premium (cost more).