Well, it turns out I didn't need as long as I thought, and I just started my Poison-type run.
Here's what I've accomplished thus far:
-Started game.
-Picked up Surfboard (Mudkip) as my starter. I'll be using him as an HM slave later on.
-Got to May without encountering a single wild Pokemon!
-Fought May, Surfboard grew to lv6.
-Got Pokedex.
-Caught 2 Zigzagoon as "Pickup slaves."
-Went from Littleroot to Rustboro. Did the usual story-related activities, fought as few trainers as possible.
-Arrived in Rustboro with Surfboard at lv10.
-Fought Roxanne (and gym trainers), Surfboard grew to lv14 in the process.
-Did usual Rustboro quests (the Devon guy and the Aqua grunt). Surfboard grew to lv15.
-Headed to Dewford, went immediately to the cave and caught Dracula, a lv7 Zubat and my first real team member.
-Backtracked to fight the trainers I skipped.
Some notes:
-Zigzagoon's Pickup. I had never bothered with it before, but with only 2 Zigzagoons, at this point, I've already acquired a Full Restore, Rare Candy, 2 Nuggets, a Full Heal, and an Ultra Ball. I'm definitely keeping the Zigzagoons in my party, at least for the time being.
-Zubat is very difficult to train from the level it's at. The only attacks it knows are Leech Life (a 20-damage, non-STAB move) and Supersonic (with only 55% accuracy, it can't ever be counted on). I actually had to use Surfboard when faced with a lv8 Taillow because Dracula couldn't do much of anything against it. Hopefully this will be the last time I need to use Surfboard in battle. I'm going to grind Dracula on wild Pokemon until it learns at least one better move before I try fighting any more trainers.
Current team (I'll only list details of my actual team members):
Dracula/Zubat
---Level 9
--Moves:
-Leech Life
-Supersonic
-None
-None
Surfboard/Mudkip (Future HM Slave)
Zigzagoon "Pickup Slave" x2 (No nicknames)
Potential Future Team Additons: Gulpin, Tentacool, Seviper (Feel free to suggest more)