Hello Multifunctionalhusband,
Your new home sounds great!
As the others said, it would be wise to eliminate the Zinsco. I worked industrial & distribution and encountered many Zinsco serving office spaces, mostly Q-Series. Lots and lots of problems arose- even back when they were new. I saw no fires that left the enclosures, but the fires burned all wiring inside the enclosures.
Also note that purchasing a replacement circuit breaker might be difficult. They are becoming harder & harder to find. (Perhaps that is a good thing. You can sell the bus bars and breakers on eBay or Bonanza for some quick money!)
Here's A Silver Lining-
Can you negotiate a discount on the home price due to the pending service work? Note that some insurance companies will not insure when Zinsco (or FPE Stab-lok) are in the building. That's a bargaining point for you.
Brand?
My preferred brand is Eaton Cutler Hammer. Bolt-on is ideal, but snap-in are also excellent. As mentioned by others above, Square D is great (QO being superior to Homeline). Siemens is also excellent.
Important-
Once you do replace the load center, contact your insurance company. I did a few "friends and family" freebies where I replaced FPE or Zinsco load centers. The home owners received a lower home insurance premium due to reduced fire hazard.
Very Important-
And Absolutely, Positively, Certainly make sure the electrician is licensed, insured and takes out permits. When the job is complete, ensure that the AHJ inspects and issues a Green Tag. (If this will be a DIY job, be sure to get a Homeowner's permit and have your work inspected.)
A Good Plan-
If I may step beyond your inquiry, should you replace the load center consider what the current service ampere rating is. You may wish to upgrade for the future. Perhaps you will someday want, for example, an electric vehicle or something in the fun stuff category (central air, hot tub...)
Again, congratulations on finding a great home! I hope you guys love it!
Paul