"Black polyethylene" seems to commonly refer to HDPE pipe, which is pretty comparable to PEX. "Just" PE pipe is cheaper and less durable than HDPE - I'd advise against that underground.
PEXa ("Uponor/Wirsbo", "ProPEX", "F1960") is the best option, especially underground and in places with a potential for freezing, since it simply expands and contracts instead of bursting and leaking. However, PEXa is a bit more expensive and requires "expansion" style fittings, which while they are most reliable and free-flowing of all PEX connections, typically require more expensive tools that may not be worth it for a one time job if you can't rent them.
PEXc is the more common and typically cheapest form; connections are commonly "crimp" or "clamp" style which are more restrictive than expansion style, but the tool tends to be cheaper. PEXc will also expand and contract, but to a far lesser degree before risk of splitting.
Ultimately, PEX is the best option these days, but the type of PEX is more dependent on your situation.
- If you plan to do more plumbing in the future and/or the pipe could be subject to freezing, PEXa along with Milwaukee's expansion tool (Milwaukee #2432) is the way to go for worry-free connections. There are also hand tools available for about half the price of a used Milwaukee kit ($160-200 on eBay at the time of writing).
- If you can't rent or find the expansion tool for a reasonable price, or are simply more budget minded, PEXc using crimp or clamp style connections is likely the best path. Home Depot near me rents the tool for $16/day.