3rd Gen Advice for New Run

So I decided to do a solo run using only Bulbasaur, no evolving. So I was wondering what kind of tips people might have, especially concerning movesets and good, low-level HM slaves. I don't want to worry much about EVs and IVs, since it takes too much effort considering I'm playing the whole game with this Bulba. Any tips?

Right now, the moveset I'm considering is:

Sludge Bomb, for anything that resists grass
Toxic, for DOT damage
Leech Seed/Synthesis for HP recovery
Razor Leaf for a grass STAB move

Any suggestions?

The moveset looks fine to me. Only change I would do is replace Razor Leaf with Giga Drain, but it would require few PP boosters to work properly. I would also consider Growth, but I don't think you would have time to set it up.

As for EVs, there really isn't much to do for Bulbasaur, as he'll mostly use his Sp.Attack, but Poison attacks are considered physical in Gen III, so it might be a good idea to stop at Route 22 and beat few Mankey. Other stuff (aside from Nidoran) on this route gives Speed EV, which is also nice to have.

But general idea for this type of challenge is to hit hard and fast. You'll have level advantage, but won't really have type advantage for most of the major battles. Rival's Charizard will be the worst opponent as it will be faster, stronger and will have advantage over you.

Buy a lot of healing items and if you ever get to the fight you know you won't be able to beat with pure power, use Toxic and Leech Seed and heal until you win.

And the most important thing of all: Don't forget to create Challenge Log for this run.

As far as HM slaves go, Krabby makes for a good one, as it gets Cut, Strength, and Surf, although you have to wait until you get to Fuchsia City to get the Good Rod needed to catch one. If you want/need things that can do the HMs earlier, you can kind of just look at the pages for the HM moves to see what learns what and just grab whatever comes first that learns the HMs you need at the time until you can get Krabby+something to Fly on.

Good HM slave is Nidoqueen or Nidoking. They can learn the three major ones in Cut, Strength and Surf(yeah a Ground Type surfing...). They can be caught relatively early and their lower forms can learn Cut and Strength. Will need to fully evolve them to add Surf to its HM list. Flash isn't really needed seeing as you can get by Rock Tunnel without it. As for doing a solo run, your biggest threat will be Flying, Fire, Dragon, Poison and Psychic. Your rival's Charizard fits two of those typings and unfortunately is immune to a move I would have suggested in Earthquake(which crushes Fire, Poison and does decent damage to Psychic since its Physical, not Special). As a result, Sludge Bomb is arguably your best offensive move for it to go along with Giga Drain(HP replenish. Just up its PP), Toxic(if you want to outlast the enemy) and Earthquake. Ice will cause you issues too but the bulk of Ice Types in Kanto are also part Water, hence go down relatively fast. Only Jynx will give you problems being part Psychic.

TLDR, heres the moveset I'd use:

Giga Drain(boost its PP)
Toxic
Sludge Bomb
Earthquake

You'll still have issues with Flying Types(which Charizard, Pidgeot and Gyarados happen to be) and Agatha's Ghosts(which have Levitate in FRLG) and are immune to being Poisoned(which makes taking them down that much harder). Lance's Dragons will give you issues too but Poison can do wonders on them. Just won't get much recovery since Dragon resists Grass. Good luck!

PS: That's if you were evolving all the way to Venusaur. Seeing as you want to keep Bulbasaur, Earthquake is unavailable. In its place, I'd use Hidden Power(which may grant you a Typing that is beneficial(Rock or Dark come to mind), Secret Power(Normal Type move with secondary effect) or Return(powerful due to high friendship). You will need something for Agatha's Ghosts and unfortunately none of your moves are that effective. Leech Seed is another option to slowly whittle them down over time but that's not effective without burning through gobs of healing/status items.

Sunny Day
Solarbeam
Synthesis
Toxic

To me Giga drain's lack of PP makes it a bit of a bad move. You have healing via synthesis and sunny day makes it even better, naturally adding solarbeam when using sunny day makes sense and toxic is good for things which resist grass. I actually prefer Razor Leaf to Giga drain because of PP, power difference being only slight and that chance of a crit.

Edit: I shouldn't skim read things.

Seeing as you're soloing, Sunny day will cause you issues with Fire types.

Toxic
SludgeBomb
Razor Leaf
Growth/Double Team.

If you're only using Bulba, chances are it'll be extremely overleveled and just cream through everything. Healing moves aren't really that necessary in a solo run because you'll have more potions than you can handle. Unless you've put some sort of rule in about healing, In which case your original moveset is perfectly fine.

just a head's up, but assuming this is FRLG, just know the sludgebomb TM is in the post game. idk if you like to have your movesets finalized on the first E4 go around like i do so just wanted to advise you of that. otherwise, your moveset looks fine. i mean, it's in-game, you can't go too wrong with whatever. i advise leech seed over synthesis just bc that's a fun way to mess w your opponent + you can use items so HP recovery moves on your pokemon aren't that big a deal.