The original BG1, BG2, and expansions had random encounters when going to rest & at some other predetermined to/from travel points. They were usually balanced (depending on your chosen difficulty) fights. Also in some encounters you would meet NPC's, sometimes fellow adventures from The Forgotten Realms universe, or find something while looting, that could start a long side quest chain usually culminating in major battles (finding Bruener Battlehamer's Pink WarHammer was one I remember because I was only ever able to get it to trigger 1 or 2 times, and there was a super hard Demi Lich battle I remember as well).
The side quests usually rewarded with major exp, loot, and usually a very hard battle with sometimes legendary loot . The encounters were random and/or sometimes tied to resting at camp or at certain inn's or at a home (like the Pocket Planer Sphere) while a certain level or level range, traveling between specific destinations, starting or finishing specific quests, or a combination of the above.
I'm pretty sure in BG3 we will meet and possibly get as an NPC Minsc. He is a seemingly slow (low Int, decent Wis), or possibly insane, due to his almost extremophile like 'lust' wanting to uphold justice, goodness, and heroism", Human Ranger from Rashemi. Rashemen are basically natural born Berserkers (so he is basically a Berserker Ranger.) He is mentioned in a reward/wanted poster or maybe letter/note you can find at Waukesha Rest. He mentioned in BG3 as the "Beloved Ranger Statue holding a small hamster in his palm that was stolen/missing", I think there is a earlier date than 1492 on the letter but I can't remember.
It was rumored in Forgotten Realms Lore Minsc & Boo were Petrified after BG2 before Decent into Avernus to either make the statue or by accident. Which is perfect timeline Match up it was around 1480 he was freed from stone, encased for about 100 years, he did some adventuring etc, then he went to Avernus on accident with Elturel 1492, BG3 takes place a few months after the return during the "Teeth' ling" exile.
His ranger animal companion was Boo, a 'Miniature Giant Space Hamster.' In BG3 they are mentioned in the book "A Primer on Mythical Beasts", found behind the bear that Volo is talking to, as being mythological or cryptid beasts. In the book it mentions "well muscled human male as their steed of choice" (describes Minsc perfectly) and "rumour claim they have a taste for human eyes" (Again Minsc would randomly tell Boo "Go for the eyes Boo!")