Happy Sunday everyone!
To contribute to the Question: Is it right for a man or a woman to get engaged before being baptized?
Being baptized has nothing to do with being engaged.
One can be baptized at anytime he accepts the teachings of Christ and surrender to the will of God, before or after being married.
There's no scriptural backing for one to engage or marry before being baptized.
We see in scriptures where a believing woman married an unbelieving husband, meaning the were not forced to marry and baptized, as recorded in 1 Corinthians 7:13.
And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him.
Now, to baptize is to follow the will of God, as we see in Acts 22:16,
And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
While to engage is to fulfill the desire of the flesh, as recorded in 1 Timothy 5:11.
As for younger widows, do not put them on such a list. For when their sensual desires overcome their dedication to Christ, they want to marry.
So being baptized can come before or after being married.
You may as well watch my contribution in the video below:
To participate, you can watch brother 
This is my contribution.
Thanks for reading.