You've picked a great decade - fifties clothes are fabulous and still very wearable.
I know you're not just interested in vintage but that's my thing so I'll stick mostly to that. I got into it in the mid '70s when I was 18 or 19 and wandered into a second hand clothes shop (they weren't called 'vintage' then) and was hooked. I've been into Edwardian, 1920s, '30s and '40s too but they're getting very hard to find now so I now focus mainly on 50s and early 60s. I love the tailoring from that time and seek out mostly jackets and coats which I wear with jeans - I don't do the whole 1950s look but, if that's your thing, go for it.
I used to buy from vintage shops and charity shops but they mostly sell Y2K now so I reluctantly (because I much prefer a real shop) signed up for Vinted and Ebay which is where I mostly buy now. I find that vintage Ebay has more professional dealers so prices are slightly higher but they're generally also more reliable e.g. about giving garment measurements and some of them even accept returns. Vintage Vinted is total chaos but quite good fun. I stick to the lower priced stuff - my most recent jacket was £5. 1950s sizing was very different to today - on average about 2 sizes smaller. You need to know your measurements and check garment measurements. If the seller doesn't give them, I ask (unless it's a fiver or less in which case I might take a punt if I like it).
One of the biggest risks of buying this way (especially from non-dealers) is that sometimes the clothes smell. I'm not talking about that musty mildew smell - I can normally fix that. It's those perfumed conditioners or laundry sprays which some sellers use heavily (possibly to cover up mustiness) and which absolutely stink and can be really hard to shift. It makes the whole thing a bit of a gamble which is why I avoid the higher priced stuff.
It helps to learn to spot genuine vintage, either by the style, the fabric or often by the labels (e.g. if there are fabric and care labels, it's probably not 1950s). I've picked up most of what I know by trial and error but, if you enjoy reading up about it, I think the most useful book I have is 'Vintage Fashion, a Sourcebook' by Nicky Albrechtsen and which covers the 1920s-1980s.
Hope some of that is helpful - ignore anything you don't need and, above all, enjoy.