Where you want to hunt all boils down to what you want to hunt.
Before the first gym, I feel like there aren't many good options that you would end up keeping to the end of your playthrough, but I'll still give my suggestions.
In terms of sheer variety, Routes 116, 102, and Petalburg Woods have the most Pokemon in them if you just want to run around and hope for the rare spawns, even if most of the time you'll be getting Zigzagoon, Wurmple, or one of Wurmple's evolutions (Petalburg Forest). However, since a lot of the routes have Pokemon like Zigzagoon and Wurmple as common encounters which you most likely won't be using for your entire playthrough, it's unlikely you'll get what you want if you're going for something a bit rarer.
That brings me to the next option, the DexNav. If you haven't played ORAS before and you don't know what it is, you get it early on and it allows you to search for Pokemon you've already caught, which is extremely helpful for getting those rare encounters like Ralts or Shroomish and I would HIGHLY recommend this. The DexNav also has a chance of forcing Pokemon to be shiny but it's a bit complicated so I won't go into it here, I recommend looking up a guide or some videos, but the very dumbed down version is higher search level = more chance for game to force shiny. As for using the DexNav itself, although you can chain Pokemon, I wouldn't recommend chaining (since it can be easy to overlevel when you defeat every Pokemon plus limited money and lower levels means less Poke Balls and more PokeCenter trips), but instead, do an encounter, run away, go out of the grass and run in circles for a bit, then search again for whatever you're hunting. You miss out on some of the benefits of chaining by doing this and it can take some time to learn if you're new to it, but overall, the DexNav is still a very efficient method to hunt for something specific.
If you don't care about getting Pokemon like Zigzagoon, you could also use a Pokemon with Sweet Scent to force Horde Encounters. At this point in the game, Surskit is the only Pokemon to have it, and you will have to find one and get it to level 9, so this is a bit of an inconvenience, but still decent if you want quicker encounters. A lot of the variety does go out the window, but some routes have better encounter rates for certain Pokemon, even if by a little, so that is something to consider. Additionally, Rusturf Tunnel has only Whismur by random and horde encounters, if you really want to use Whismur for some reason.
Overall, DexNav is the best option if you're going for a specific target. Since some of the early game options aren't too great, I personally wouldn't bother with random/horde encounters, unless you really want the random aspect of it. Again, where you hunt all boils down to what you want to hunt, so planning out your team in advance can help with finding where and how to hunt.
I hope this helped and good luck with your shiny hunts.