It isn't at all obvious why 'handbasket' was chosen as the preferred vehicle to convey people to hell. One theory on the origin of the phrase is that derives from the use of handbaskets in the guillotining method of capital punishment. If Hollywood films are to be believed, the decapitated heads were caught in baskets - the casualty presumably going straight to hell, without passing Go. That's a nice theory but fails a pretty basic test - guillotines were invented in the 18th century and the phrase dates from the 17th.
The first version of 'to hell in a handbasket' that I can find in print comes from the Weekly pacquet of advice from Rome: or, The history of popery, 1682:
"...that noise of a Popish Plot was nothing in the world but an intrigue of the Whigs to destroy the Kings best Friends, and the Devil fetch me to Hell in a Hand basket, if I might have my will, there should not be one Fa∣natical Dog left alive in the three Kingdoms."
https://www.phrases.org.uk/meanings/hell-in-a-handbasket.html
Damme, concludes the fourth man, that story of Godfrey's being
Killed at Sommerset-house was all Bubble; why the Divel should
the Papists meddle with him? the three poor fellows were meerly
sworn out of their Lives, and so were all the rest; that noise of a
Popish Plot was nothing in the world but an intrigue of the Whigs to
destroy the Kings best Friends, and the Devil fetch me to Hell in a
Hand basket, if I might have my will, there should not be one Fa∣natical
Dog left alive in the three Kingdoms.
https://quod.lib.umich.edu/e/eebo/A69775.0001.001/1%3a31?rgn=div1;view=fulltext