Proper

Suited or acceptable to the purpose or circumstances; fit, suitable. [13th c.]
Following the established standards of behavior or manners; correct or decorous. [18th c.]
a very proper young lady

(grammar) Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter. [14th c.]
Pertaining exclusively to a specific thing or person; particular. [14th c.]
(usually postpositive) In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).
(archaic) Belonging to oneself or itself; own. [14th c.]
(heraldry) Portrayed in natural or usual coloration, as opposed to conventional tinctures. [16th c.]
(mathematics) Being strictly part of some other thing (not necessarily explicitly mentioned, but of definitional importance), and not being the thing itself. [20th c.]
(mathematics, physics) Eigen-; designating a function or value which is an eigenfunction or eigenvalue. [20th c.]
(heading) Accurate, strictly applied.
Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.) [14th c.]
(now regional) Attractive, elegant. [14th c.]
(often postpositive) In the very strictest sense of the word. [14th c.]
(now colloquial) Utter, complete. [15th c.]

Synonyms

(fit, suitable): correct, right, apt, prudent, upright, sensible, fitting

(correct, decorous): appropriate, decent, good, polite, right, well-mannered, upright

(fitting, right): appropriate, just, honorable

(complete, thorough): comprehensive, royal, sweeping, intensive

(strictly, properly-speaking): strictly speaking, properly speaking, par excellence

(true): full, complete

(informal: utter): complete, right (informal), total, utter

Antonyms

(fit, suitable): incorrect, wrong, bad, imprudent, insensible, improper

(correct, decorous): inappropriate, indecent, bad, impolite, wrong, ill-mannered, unseemly

(fitting, right): inappropriate, unjust, dishonorable

(complete, thorough): partial, incomplete, superficial, slapdash

(true): incomplete