are the probes that are included in the kit good and all that's needed for basic measurements?
The Rigol DS1054Z includes four RP2200 probes, one probe per channel. Those probes are passive probes, switchable between 1x and 10x. At 10x, they have 150 MHz bandwidth (bandwidth at 1x is much lower, as is typical for a passive probe).
They're typical general-purpose high impedance voltage probes for this type of scope, and should be good for most basic measurements.
Like this Rigol, most new scopes in this bandwidth class will come with passive 1x/10x probes similar to these, usually one per channel. Note that if you're shopping for used scopes, many won't include probes, and if probes ARE included, they may be beat up. Replacement RP2200 probes list for $33 apiece in USD, meaning that getting four new probes would cost around 1/3 of the list price of a new scope.
There are other kinds of specialty probes, like current probes, high voltage probes, differential probes, etc. These may be useful or essential for some types of work, but they're not typically included in the standard kit of an oscilloscope. Some specialty probes can be very expensive.