Short answer: Best use lowercase in method
attributes of <form>
tags.
Long answer: It slightly depends on the HTML version:
HTML5: The html5 living standard states that lowercase get
maps to the HTTP method GET and that lowercase post
maps to HTTP method POST [1]. However as of today, enumerated attributes match case-insensitive [2]. So you could in theory use any casing. I am pretty sure this was different a couple of years a ago, but that's the nature of a living standard. The examples in the HTML5 standard use lowercase. So, if you follow HTML5 standard, I would recommend to use lowercase, even though it does not really matter.
XHTML: Use lowercase. The DTD of xhtml-strict and xhtml-transitional only define lowercase get
and post
[3, 4]. Here its is even more important, as using uppercase will produce an invalid XHTML document that can trigger ugly browser errors in practice (depends on DTD, browser and http content-type).
HTML 4: In these days, it was common practice to use uppercase, but lowercase also worked well in practice. This is just my personal experience, I am not going to look up the HTML 4 standard as it seems irrelevant nowadays (and nobody ever followed it strictly anyways).
[1] https://www.w3.org/TR/html5/forms.html#attr-fs-method
[2] https://html.spec.whatwg.org/multipage/common-microsyntaxes.html#enumerated-attribute
[3] https://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd line 695
[4] https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd line 888