Baby bottle sanitiser is just slightly diluted bleach, so no benefits there, just more expensive for the same thing.
The problem with bleach is that it takes 15-30 mins to work, which can be a pain when bottling etc. You can also get contact sterilisers which work immediately. They are more aggressive towards you by their nature, so require a little more care.
The two most commonly used are videne and star-san (or something similar). Videne is available from decent chemists, but they'll need to order it specially. I'm not sure with star-san. Both need to be acidified to work properly, some come mixed with acid already, others will need to be mixed with ideally phosphoric or hydrochloric acid, but citric acid will do otherwise. Vinegar would be no good at all for this.
Aleman uses peracetic acid, but that's horrible stuff and unless you know exactly what you're doing is best avoided.
For other general cleaning, a non-scented oxidising laundry bleach (usually called something like oxy-action or the like) is very useful, contains hydrogen peroxide, a strong oxidising agent, and some surfactants. Very good for lifting stains and killing anything hanging on.
Tim