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I have a female Aerodactyl in Leaf Green. It is level 5 and has Calm Nature. And here's its stat spread currently. 23 HP / 14 Atk / 11 Def / 11 Spa / 14 SpD / 18 Spe.

My question is, how can I get an Aerodactyl with good/perfect Atk and Spe IVs? And, who is the most suitable mate for it? I'm not breeding for the moves I want. I'm breeding for good/perfect IVs.

Since there's no guaranteed way to get a Pokémon that has good IVs in 3rd gen... I'm not sure how you could get a baby Aerodactyl with good IVs.

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IVs vary from Pokemon to Pokemon. It is not like some Pokemon definitely have better IVs than others. For example, a Sunkern can have all 31 IVs in all six stats and something like Aegislash or Ash-Greninja or any Uber mon can have 0 IVs in all six stats (Most legendary Pokemon caught in the wild have at least 3 perfect IVs but I'm talking about breedable Pokemon, or on PS!).

Thus, any Pokemon with a compatible egg group is fine, as long as it has good IVs. This unfortunately is generated at random, and you have to really lucky to have perfect IVs in the stat you want.

The gist of what I'm saying is, it doesn't matter which Pokemon you use, because even a Pokemon with crappy attack is still useful in breeding if it has perfect (30 or 31) IVs in the Attack stat. So, you just have to check which f your Pokemon from the same egg group as your Aerodactyl have perfect or near perfect IVs in Attack and Speed. Generally, it is a bonus if it has good IVs in Hp and both defenses too, for maximum survival. Having perfect IVs in Special Attack is a waste as far as Aerodactyl is confirmed.

tl;dr : IVs are independent of species of Pokemon, they are unique to literally every Pokemon, in the sense a Pokemon can have any IV in any stat independent of its stat or total. Look for a Pokemon with perfect IVs in Attack and Speed for Aerodacytl

Finally, get it to hold a Destiny Knot, to ensure (or at least, vastly increase the chance) that the baby Pokemon gets the IVs in the stat you want.

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I heard that some IVs are inherited. Does that mean it will be the best if I get another Pokemon with good Atk/Spe IVs to breed with Aerodactyl? I still don't understand and I'm just a rookie in breeding IVs and stuff.
Also, isn't Destiny knot unobtainable in Gen 3? I thought it was from Gen 4 onwards.
My bad, I didn't see your tags. Yes, you're absolutely right, Destiny Knot is not obtainable in Gen 3.
IVs ARE inherited. That means if you have a parent Pokemon with good IVs, then there is a chance that 3 out of 6 of those good IVs are passed on. The other three are from the other parent Pokemon, i.e. your Aerodactyl.

But, a Pokemon has IVs at random, and you can't be sure that any particular Pokemon has better IVs. It literally depends on your Pokemon and there are no external controllable factors that dictate that a Pokemon MUST have good IVs. It's all a matter of luck, to be honest. You just have to keep trying!
Also, out of curiosity, why are you breeding for competitive battling in Gen 3? No offence, but it's much easier to do so in the later Generations (6/7). It is kind of hard to get a perfect Pokemon in FR/LG or R/S/E. So, is this for personal satisfaction, or like a bet between friends to battle competitively against each other using Game Boys or something? Please don't mind my curiosity, I haven't seen people trying for perfect IVs in the older games, as meta battling is ever dynamic, changing generation to generation. Competitive battling from older generations is pretty much obsolete, so I assume this for collection purposes?