This is one of those places that plastic has some real advantages.

Just make sure you use a type your AHJ will allow.

The direct buried water line from the municipal main or well to the structure is technically defined as the "Service Line"

Under the UPC (Uniform Plumbing Code) you may use;
Asbestos Cement Pipe, Brass Pipe, Copper Pipe-types K-L & M in both hard drawn rigid lengths and continuous roll pipe. CPVC pipe, Ductile Iron Pipe, Galvanized Steel Pipe, PE Tubing(Polyethelene tubing-commonly called roll poly or black poly pipe), PEX plastic tubing,PVC pipe

Under the IRC (International Residential Code) in addition to those materials listed for the UPC, you may also use; ABS Pipe, PB Pipe(Polybutelene Pipe) and PEX-AL-PEX pipe.

In the real world, I doubt if you could even find a source of supply for Asbestos Cement Pipe and while it could be said to have an infinite service life the labor & material cost of brass pipe makes it cost prohibited.

Prior to the invention of plastic pipe Galvanized iron pipe and ductile iron pipe were the mainstays of the industry, but here again, due to the cost of metals and the high degree of labor required to install them, they are also considered cost prohibitive, not to mention that they are highly subject to mineral scaling that will effectively reduce their working diameters in a relatively short time. It must also be noted that when running iron pipe under a slab the pipe must be machine wrapped and all joints must be field wrapped to the same level of protection.
While the IRC does allow the use of PB pipe due to the extrememly high incidence of failure in the fittings there were massive class action suites against it in the late 1980's and early 90's and I don't know any reputable plumbers who will risk using it.
PVC, CPVC and rigid Hard Drawn Copper Pipe are approved under both codes, but those are rigid length pipes which would require a joint every 20' and at each change in direction. Understanding that most failures occur at joints it would then stand that a continuous roll material that is free from joints might prove to be a better choice.

The choices then come down to PE Pipe (black poly), PEX pipe and roll copper pipe. All of these materials are available in 100ft rolls so you could make your entire run free of excess joints. Roll pipe is also much more forgiving if your trenching is uneven, although all pipe laid in a trench should be sand padded both under the pipe and above it before backfilling.

For economy and proven service life my personal choice would be PE Pipe (black poly) with brass barb fittings and stainless steel hose clamps on the fittings but be careful here, in some jurisdictions they require a minimum of 10' of copper pipe in direct contact with earth to insure the water system is electrically grounded and in one jurisdiction near me they require all service pipe to be copper.

It should also be mentioned that when copper pipe is run under a slab all joints must be brazed, not soldered. Personally, I braze all copper joints intended for direct burial.

If you will submit a list of all the plumbing fixtures in your house, I.E. sinks, tubs, WC, laundry hookups etc, I will be glad to work up the load and determine the proper size of line needed for your structure.

Thanks for the detailed answers!

You still need to talk with your AHJ or water supplier.

The model National Codes are NOT always adopted as they are written by the national authorities.

Each adopting authority can make changes.