Base layers are items worn between you and your costume to help keep you cool, hygienic, and extend the life of your fursuit between washes. They follow the same rules as balaclavas, you want to get the ones made for hot weather, which are typically made of lycra or spandex/elastane. UnderArmour still uses the name “HeatGear” for this type of clothing if you want to go with that brand specifically. But typically, almost any “athletic gear” should serve as a good base layer for fursuiting. Compression is not necessary for a base layer, but it does not need to be avoided. An alternative to “athletic gear” are “rash guards”, which may be slightly cheaper in price.
I have personal experience with UnderArmour (it’s good and worth the price in my opinion) and GearX (Definitely good for the price, but I prefer UA). Some other brands have been included below but I have no direct experience with them. It appears GearX is no longer sold on Amazon, but TSLA/Tesla looks identical, so I assume it is the same manufacturer.
A note on one-piece base layers, such as dive skins: Some people swear by one-piece suits for fursuiting. I have personally tried a dive skin and although it has its uses, having separate pieces is wholly easier in my opinion. That being stated, if you are looking for a one-piece layer, a “zentai suit” is the cheaper option, whereas a “dive skin” is the slightly more expensive option. It is important to note that a dive skin is not a wetsuit. A dive skin is put on beneath a wetsuit. Do not wear a wetsuit under your fursuit. If you like the idea of a dive skin but don’t want to actually get one, rash guards are often made of the same material and thickness.