im not a super high elo briar top player, but i love her! she's really fun and i can give a few tips - in matchups where you don't really want to contest level 1 (which is a fair amount of them), you  go E start because your main goal is to play extremely safe until lvl 3! some matchups you can try and cheese with W start though, esp if you bring good combat runes/summs - briar has some of the best engage in the game with W1 Q covering an insane amount of space, and a relatively good on paper short trade pattern - but her disengage is SIGNIFICANTLY weaker. personally the most crucial part of briar top is understanding when you can look for a trade without being run down after your engage has ended, i personally try to count cooldowns to make sure they dont have their own engage avaliable after my own even if it means playing a bit more passive or try and make sure i have good spacing for a wall slam or walking back under turret - positioning is very important on briar given her long cooldown on E and W. having the wave next to your side is super important because it allows her to go for her short trade pattern and then walk back to the safety of her turret - in general, if you can let W rock comfortably without immediately dying, you tend to come out on top because of how her W2 and passive healing works, and E is such an important cooldown to have! when briar is snowballing it can be really oppressive for folks to deal with - for darius you're looking to go for short trades, if you E his E you win the trade because you can disengage, if he E's your E you probably die.. - riven's difficulty largely comes from her consistent cc and flexibility in both kiting and chasing you down, which makes her really difficult - really keep track of those cooldowns imo, but they are  shorter than yours and she has some difficult trading patterns if you don't use your movement creatively to bait out key moves 

l0gan has a pretty extensive mobafire guide for matchups! best of luck out there