If unavailable, I was told to purchase the Rigol DP832A instead to be more cost efficient and sidestep Rigol DP832 bugs/firmware errors.
Are they not the same power supply? I'm also under the assumption that the DP832 is close to being phased out.
They are the same supply and the statement that buying the DP832A would let you sidestep the DP832 bugs is 100% incorrect. The DP832A is a DP832 with all options built-in, plus a colorful front panel and multiple colors enabled on the display (the display of the DP832 is full color but the firmware only has monochrome themes - you pick the color). I don't know if these will be discontinued soon. They are still excellent for the price and many people have them (and they are reasonably quiet, once you've swapped the fan...).
As for the "consistency", I am not sure it is important or useful. I started this way (DP832, DS1074Z, DG1022...) and the DG1022 (not Z) ended up being a disappointment, so I sold it and went elsewhere. Since then, I have also upgraded the scope, so I am left with just the DP832. I wouldn't necessarily try to stay with Rigol as you will be upgrading later based on needs and availability of new products, so it is very unlikely you'll stay with Rigol forever and instead will end up with a mix.
Instead go for bang-for-buck and look at competitors. Look at used gear from 1st-tier companies (Keysight...) as this may work out better.
Note that you may not need a bench DMM at all (get a good handheld first) or a function gen (get a $20 EBay one to start). With time, you'll figure out what you need exactly. For instance, if you do a lot of work with microcontrollers, you may find you need a USB Logic Analyzer first.
The absolute only reason to go all-Rigol is if you really want to install their (mostly dreadful) PC software as it forces you to install the NI Visa stack, which sometimes causes issues with other instruments Visa stacks. OTOH, if you only want to run C/Python/Matlab SCPI scripts, it doesn't matter.