It depends on who you are quoting, and for what purpose. In normal writing, it is fair to assume that your source wrote in coherent sentences, which include a capital letter at the beginning and a full stop at the end. So long as this goes within the inverted commas, the sentence does not need re-punctuating. A partial sentence does not (necessarily) require either, but does require an ellipsis [...] to show it is partial. (So if you quote 'everything except the full stop', you end up with 3 dots rather than 1.)
On SE the rules are a little less formal, particularly if you are quoting yourself. If you think your quote would be better without the full stop, go ahead: you presumably won't be misquoting yourself.
The punctuation is the same as for any other clause: you need a comma after the quotation only because you put one after 'such as'.
(PS I use British rules for punctuation and inverted commas: US rules are sometimes different).