I grow outside, so I hate garlic, because it attracts grass hoppers, which are way harder to deal with then aphids or mites. If you've seen my grow photos you know my property looks like a field. I've had to deal with ticks, aphids, mites, horn worms, moths, slugs, snails, gnats, grass hoppers, mice, etc. What works for is a good integrated pest management plan. I start off using food grade Diatomaceous Earth and soapy water. I'm not 100% organic, so I don't mind using Dawn dish soap instead of buying Yucca Extract as a surfactant or wetting agent.
For the most part, soapy water and DE is all I need. Other pests do come around, but as long as my plants are healthy they can dish it out, plus by not constantly spraying my plants, I allow natural predators to come in and keep populations under control. In fact, I'll often grow plants specifically to attract or act as a shelter for beneficial insects. Carrots and cat grass are really good for that.
Sometimes I do need to remove pests, so the first thing I usually turn to, especially early in the season, when temperatures are cool and it's rainy, is horticultural oils. Neem is a popular one, but I happen to like oils that contain 5% sesame oil or even Tea Tree Oil, but that's just personal preference. After a spray of oil, I'll go back to the soapy water and DE method. Sometimes I'll introduce lady bugs into the garden if their populations are low, but I haven't needed to do that in years.
Since oils only kill by suffocation and tend to evaporate within hours or days, they are extremely safe. However, sometimes I do need something that lasts a bit longer. That's when I have to really think about the next step. If its still early in the season and things are looking really bad (maybe because my neighbor isn't doing his job or the weather was just ripe for an infestation to sweep through) then I'll look into using Carbaryl (Sevin %5 dust as it's more commonly known). Carbaryl is very powerful, because it's a true poison, but yet it's still safe to use around pets and children. It's one of the few poisons that you can actually use in an organic settings, under certain restrictions. I often use it against grass hoppers, since that's about the only thing that kills them in large numbers. However, it's best to use carbaryl in traps or in very selective areas. Since it's so powerful, it can very easily wipe out all the good insects, which has been known to cause outbreaks of mites and aphids.
If using carbaryl isn't warranted, I'll go with a pyrethrins based insecticidal soap. Like oils, it only lasts a short time, but unlike oils, even when diluted, its still a very good insect repellent. Pyrethrins usually lasts a few days to a week and can be used much later in the season then carbaryl. Pyrethrins are one of the safest insecticides, but because it's so widely used (both in the garden, on pets for flea & ticks, and for humans to treat lice) many insects are becoming resistant to it. However, if you use it as part of your overall Pest Management Strategy then you shouldn't have to worry about this.
Again, rather then relying on one signal product to kill everything, you want to have a multiple 1-2-3 knockout approach. And most importantly, it's also important to remember that healthy plants are less likely to be damaged by insects. And most of the time, if you just leave your healthy plant alone, other insects will do the job for you. So don't freak out because you found a few holes in some random leaves. Freak out when the pests are in such numbers you can easily ID them from any angle of the plant and they actually causing a problem.