The usual go to verse for what is the essential doctrine that a person must believe is something like John 3:16, 1 John 5:1, or Rom 10:9:
9 If you declare with your mouth, “Jesus is Lord,” and believe in your
heart that God raised him from the dead, you will be saved. 10 For it
is with your heart that you believe and are justified, and it is with
your mouth that you profess your faith and are saved. 11 As Scripture
says, “Anyone who believes in him will never be put to shame (The New
International Version. (2011). (Ro 10:9–11)
The main concept is that while man had fallen into a state of sin and damnation a Messiah from God (and so yes the fact that this Messiah Jesus is God, as born of a virgin and the Holy Ghost, is included) – came to be a sacrifice for sin, so that by believing and thus receiving this gift, we become children of God.
So it is faith in God joined in humanity in Christ, by the work of his mediation for the recovery and salvation of sinners, that is sufficient to save anyone:
the Lord Christ, in the work of his mediation, as the ordinance of God
for the recovery and salvation of lost sinners, is the proper adequate
object of justifying faith
(Doctrine of Justification by Faith by John Owen page 89)
...
So, as unto his death, “God set him forth to be a propitiation,” Rom.
3:25. “He spared him not, but delivered him up for us all,” Rom. 8:32;
and therein “laid all our sins upon him,” Isa. 53:6. So he was “raised
for our justification,” Rom. 4:25. And our faith is in God, who
“raised him from the dead,” Rom. 10:9. And in his exaltation, Acts
5:31. Which things complete “the record that God hath given of his
Son,” 1 John 5:10–12.
(The works of John Owen. (W. H. Goold, Ed.)
(Vol. 5, Justification by Faith page 92))
Where this clear line might become more gray is that one can speculate who believes this core doctrine and who does not based on other believed doctrines or not. But this is not differing in what doctrine saved a person, but how is it possible they can believe this when believing also in another thing. For example as an exaggeration one could not believe the devil should be worshiped while also believing this. Or one could not believe that serial killers are without guilt, while also believing in Christ.
I have never heard anyone think one must understand the doctrine of election to believe in Christ. I think there are no other major doctrinal requirements among reformed theology but the debate comes more about the amount of virtue in a persons heart after faith. Do they show signs of loving God and the neighbors? This becomes the pertinent question for how can you love God if you do not also love his children?
As a final note, one more serious way of jeopardizing this basic faith is to add another requirement to believe in someone else. For example if one were to add a necessity to believe in another Prophet, or a Pope, or some guy who say he is important called 'Fred', 'Billy", or 'Joe', who claims to have received some new truth from an angel, then such faith will not save anyone because genuine faith in Christ must not only be in him, but in him alone:
8 But even if we or an angel from heaven should preach a gospel other
than the one we preached to you, let them be under God’s curse! 9 As
we have already said, so now I say again: If anybody is preaching to
you a gospel other than what you accepted, let them be under God’s
curse! (NIV (Ga 1:8–9).
