This has been raised as a canonical Q and A for future reference
How can I acquire electronic parts/items/modules and ensure that there is minimal risk of them being unsuitable for my project or design?
Do not assume that the product will be OK based on marketing/sales claims without researching the fine detail in the data sheet. This is why you need a data sheet, so do your homework and ensure that what you think you need is matched by the technical details in the data sheet. Make sure you have the latest data sheet (see 3 below).
The data sheet is sometimes wrong so, if something appears not to make sense, double check that you have the latest issue of data sheet and, if in doubt about some parameter or other, you can always raise a question on this site to gain clarity.
Earlier revision data sheets are usually available and so, if the manufacturer updates it, this can be traced back to the point where the change was made. Always save the data sheet in your design file when you use a new part. On the other hand, web-based specifications have no historical traceability and can lead to confusion and mistrust should things go wrong. This can make you appear stupid or careless and, won't provide the evidence that can cover you should there be customer dissatisfaction or legal problems.
The manufacturer of the part should be reputable but, as we know, new part manufacturers entering the market may not have gained a significant reputation. So, this may be hard to establish and, you have to be cautious. A lot of confidence can be gained by reading and understanding the data sheet of the part.
The supplier/shipper must be reputable for the type of goods they are handling (namely electronic parts) and, they should provide links to the manufacturer's data sheet (1). How do you know that some unmentionable supplier hasn't mishandled the goods and damaged them? I'm thinking ESD and water damage here but, there are probably other ways "unseen" damage can occur.
Watch out for fake parts – if the price seems too good to be true then maybe consider that the parts might be fake or possibly failed items underhandedly acquired by some disreputable supplier
Decide what you need to buy - don't assume that any old resistor, capacitor, transistor, or op-amp is going to work – think about what your final expectations are and, where things can go wrong (such as drift or basic output inaccuracies). You can't expect a supplier to be held responsible for you choosing a part that you haven't thought through sufficiently. This is what design is about - it's not about guessing that this or that will do so, do your homework (or pay the cost).
If you buy from a source selling unbranded goods you are taking a risk and, quite possibly, you will pay more (due to you wasting your own time) in the longer run so, how much do you value your time?
The component may be available from more than one manufacturer, in which case it is worth looking at the other datasheets as there could be some parameter which is better for your purposes in the product from someone else.
I'll probably think of a few more things to add as time passes by.