A 4Gb server is more than adequate to run a new Jira for a few people, even if you put the database server on it as well. I'd give the Jira service 1Gb memory, most database servers won't need a huge amount, and remember you need to give the operating system some space in memory too.
I would strongly recommend using a supported database. Jira ships with an internal one, which is ok for a bit of trial or testing, but can fail catastrophically without warning.
The "right" database of the four supported ones is usually easy to decide. Pick the one you have the most experience with. If you have absolutely no preference, then go with PostGreSQL, as it's the one Atlassian uses for Cloud and development. MySQL is the second choice, Oracle third, and MS-SQL a distant fourth. But that's 5% of the decision - 95% of it is "which one do you want to support"
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