I have a Trek 1.1 which is their bottom of the line road bike from 2015.  Since new I have ridden it around 1100 miles, and when I just took it in to have the bottom bracket looked at (loose & creaky) they gave me a list of things that are worn or shot on the bike.  That list included chain and cassette.  

Trek website says the cassette is a Sunrace CSR86 11-28 and chain is a Sunrace CNM84.

Should I order these exact ones to replace them or is there some other/better option I should get instead?

Sunrace isn't exactly top of the line gear.

And 1100 miles isn't much. You should get a couple thousand out of a chain, and unless the chain is absolute garbage, you should get many chains out of a cassette.

That said, a quick google search shows that to be a 8-speed setup*. You'll have a hard time finding good parts; they just don't make good parts in 8-speed.

*-And an MTB setup at that. Only after I replied did I realize that this is for a road bike.

Your cassette is probably fine.   Chains can and do wear out, especially if you’re not maintaining it regularly.  There are gauges to measure wear.
Any 8-speed chain will do fine.  You don’t need to replace it with a Sunrace.

They have a guage for chain wear. Have them show you the reading.
If you are a monster and can wear out a cassette in 1100 miles you probably already know when to change it.
Regular casual rider should be getting ~5-7k out of a cassette unless there is some type of bearing failure.
I know a guy that changes chains about 3k and cassets at around 4-5k, he is a machine, super strong and rides around 12k/year.

These are my opinions.

You could replace them with equivalent Shimano 8 speed stuff --- its not that hard to find

get a chain gauge and watch a video on changing cassette.I think my shop wanted $75 to replace a casette I did it for $19 and $15 in speciality tools of ebay