How do you make alchemy effective?
I've been playing a character with a substantial archery bend. Alchemy has played a big part of that character. It does take time and it's very difficult to gather ingredients if you consistently fast travel. But I'm constantly picking up the few common ingredients that I use for the potions and poison that I use with my archery. I don't want to spoil things, so I'll speak with some generality. Here's a list of the alchemy effects that I use and in parentheses the number of ingredients that I've commonly found in the wild or in caves have that effect:
Restore Stamina (2 and rising due to leveled creatures)
Restore Health (5 and rising)
Regenerate Stamina (2)
Regenerate Health (2)
Slow (2)
Paralysis (2)
Fortify Sneak (1)
Fortify Archery
Invisibility
Frenzy
Fear
I generally don't feel the need to use fortify sneak, fortify archery, invisibility, frenzy, or fear that often, so the lack of common ingredients matches my need for them. At this point, I'm still collecting every ingredient that I can get my hands on when I'm exploring. When I get back home from going out on a couple quests, I test any ingredient that I haven't yet tested. Then start with the ingredient that I have the most of and match it with every ingredient that I haven't tested it with. Pairings that have been tested and failed are a different color than those that are successful or yet untested. Anytime, I'm in a new place, I'll swing by the local alchemist and buy and cheap ingredients that I either know I need (I have a list of about 15-20) or don't know enough about yet.
Also, if you are having more trouble dealing with magic users than non-magic users, it may be helpful to find and activate the atronach stone. I recently switched over from the thief because I had gotten my alchemy, light armor, speech, lockpicking, and sneak to functional levels (I'm around level 20). I've read that its effect also works on dragons, but I can't confirm that because I haven't fought one since my switch. Also, I've started finding scrolls of mass paralysis in random loot. Those come in particularly helpful when I have to deal with one of those big groups. I'm not sure at what level they become findable/buyable.
There are a lot of options out there to make archery a viable play. Some of which you can see in the other comments. It does seem like a build that requires a bit of planning and a little creativity with shouts, alchemy, stealth, and tactics to succeed, but it's a build that I've enjoyed so far.