Agree with most of what's been said re credit and debit cards. Not much experience of Paypal. Credit card is good in that you have some comeback if the goods go missing/ are faulty. Use the well known names,never use links to the websites, look for the padlock, never allow card details to be saved. Take your time at checkout and scrutinize all details carefully before committing..
Not so much a security thing, but check carefully re postage and packing charges. Use google to compare the price of something you want to buy, but be aware that the cheapest option may not be so once P&P is added.
Amazon is also tricky as you may think you have reached the amount that allows free P&P but then discover that not all items are sold directly by Amazon so there is a charge after all. Having said that, I find that Amazon is usually reliable and quite often cheaper. Another tip is to create a wishlist in Amazon and put in it things that you would like but aren't in a hurry for; sometimes you will later get a notification that the price has dropped.
I haven't checked, but if you go onto Martin Lewis's website - moneysavingexpert - there will be advice on there on how to shop online safely. And remember that you have the right to return items that you are not happy with - within a certain time. That's another thing to check; some firms allow you to return items for free, and some expect you to pay for return.
Once you start doing it you won't stop!Good luck!