I'll give you the inexpensive answer--go to your local sports store and buy a tight, long-sleeve under-armour shirt. I don't know what the fabric is, but the type that has some compression. I've worn those for years, including doing no-gi and never had one rip. Some of the thin thermal type clothing for other sports works, too.
That type of thing is more common in my own experience for experienced grapplers to wear. Grappling-specific rash guards are fine, and they should be even more durable (but expensive), but when newcomers show up with fancy rash guards with a bunch of flags and MMA fight team logos on them....well, it's like a skinny guy coming to the gym with weight lifting gloves and a headband on. Not that there's anything wrong with that