What wire size do I need for a 200A residential service?

If the load is feeding the entire home it can be de rated to 83% as long as the calculated load Is below this 166A 310.15.B.7.1 (& .2) AND The ampacity of the feeder can not be below 83% so 4/0 rated at 180 amps is the minimum

The 75 degree table is used. Per NEC 110.14.C.1.b @Jack had it I provided the code references.

Yes if overhead run some think that table can be used but only if the feed has less than 24” of conduit.

The standard Al size is 4/0. Length of conductors could need larger. Ambient temp would be subject to actual installation and local amendments.

You're probably confused because the NEC keeps changing the way we get to the same answer. We used to have a Table, 310.15(B)(7). Then 2014 they took a way the table and said:

310.15(B)(7)(1) For a service rated 100 through 400 A, the service conductors supplying the entire load associated with a one-family dwelling, or the service conductors supplying the entire load associated with an individual dwelling unit in a two-family or multifamily dwelling, shall be permitted to have an ampacity not less than 83 percent of the service rating.

So then 83% of 200, Table 310.16/310.15(B)(16), 75°C conductor rating, same size as the old table.

Now 2020, Meet the new boss, same as the old boss.

NEC 310.15(B)(7)(1) moved to 310.12(B), but with new table, 310.12.