A heated basement slab requires plenty of extra planning before anything is poured. You will have to have a thermal break planned for (styrofoam is often used). Then you have to plan to have the hydronic heating tubes laid and then coated in concrete. You then have to have the concrete experts on hand for the last bit of the pour.

The concrete aggregate used as a "finished" floor is NOT the same as what comes out of a cement truck. A special aggregate will be applied at the right time during the slab preparation. The guys will have to take plenty of time smoothing and readying the concrete so that a later date they can come back and do the polishing, staining and then finishing.

As for heating the slab, it is a SLOW process to turn it UP or DOWN. On average, you can increase/decrease the temperature roughly 5 Celsius (9 F) per 24 hours. That means to turn it "off" it should take a 4 days. To turn it back on, again another 4 days. And going away for winter break? Don't touch it. Leave it be. There is nothing worse than frozen hydronic tubing that has burst because you wanted to save some energy.

I've seen $25K spent on hydronic heating installed in a basement slab. The finished concrete will add another $5 - $25/sf to the build.

And concrete in a basement is LOUD. The noise will bounce all over the place. Down hallways; up into the space above; under door jams; etc. The ceiling will require PLENTY of acoustic insulation to stop the up-down noise intrusion....especially with a "screening" room. You will want to contain the noise in the basement.

I've seen concrete floors covered up within 7 years. Most homeowners find them "too hard" to live with (both "hard" and difficult because of all the noise).

Basements typically have low heat loss (the surrounding dirt is a great insulator) and need little heating compared to the same square footage above ground, except in the tightest of houses.

Presuming you're in a mild weather part of California, putting heated floors in a basement is a waste of money. If the rest of the house has forced air, put a few ducts in the basement and call it "Done". How many and where, of course, need to be determined by the proper analyses done by your HVAC contractor.

Good luck

Your temperature ideas about our weather are far off for the temperate (coastal) parts of the region and way off for inland areas. All the same, basements (which aren't that common) still don't need much.