Hmm.
What is fortunate is that both are easy to grow, and grow well with similar needs.
I have had excellent luck with both onions and potatoes with my normal composted manure treatment. I'm not crazy about testing my soil, sorry.
I've had excellent luck with Norland Reds, Yukon Golds, and Kennebec White potatoes. Interestingly, each year one doesn't do well while the others thrive.
Yes, either mound up dirt or mulch around your potatoes. Mulch is better, dirt is good. Get yourself a potato digger if you are doing more than a 20' row of potatoes (assuming you have at least a garden tractor). You will thank me later.
Onions: I grow them in what I call 1x2 rows. I plant two rows about 1 foot apart (onions about 8 inches apart in the rows) and then each double row is spaced by a 2 foot gap to the next double row, which gives me enough room to walk along and use my long handled stirrup weeder to get 95% of the weeds. It looks something like this:
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Onions and potatoes DO NOT TOLERATE WEEDS. So weeding is paramount. For variety, I like Yellow of Parma, as it has good flavor, keeps well, and grows well here.
Both onions and potatoes need to be regularly watered. Don't let them go dry, don't have them soaking wet all the time either.
Its also bad juju to let critters and kids trample on the onions and knock the tops over. Onions don't like that....
One issue with onions from bulb sets is some WILL jump to seed. Just pull them and eat them. Nothing you can do to stop it, and the onion will start to rot quickly. You can fix this by starting from seed, but that is only a good idea if you need