I am after both too and I wanted to say It is possible to get both. Oh and they work together amazingly well!
Both have additional rate ups this year (assuming we follow JP schedule):
Nero Bride is on solo rate up in September as part of Nero-fest
Tamamo is on solo rate up during the Onigashima event in June and as a new year 2020 solo rate up.
This gives you five options depending on the amount of luck and Saint Quarts and who you like most.
Option A: get both during CCC. This requires both lots of luck and a good stash of sq. It is the fastest method. I am guessing it probably won’t be feasible for you unless you get one or the other in a single ticket/roll. And yes they do have a rate up together during CCC but Gilgamesh and Karna will also be on rate up with them.
Option B: get Bride during CCC and roll on Tamamo in June. This will be the second fastest method to get both but will require you to have a good amount of sq following CCC as you have only about a month to save. It will help you get more event CEs though.
Option C: Get Tamamo during CCC and save up for Nero during Nero fest. This gives you about 4 months to save. Probably the most efficient strategy for sq and time. Also gives you more event CEs.
Option D: Get Nero during CCC and save for New Years Tamamo. Probably the most fool proof strategy but it will take about 2/3 of a year to do. However, it has one other benefit which is relate to the next option…she could spook you while you await.
Option E: Get Nero during CCC and just wait for a Tamamo spook. Nero Bride is limited and CCC and Nerofest are the last two times to get her for the next two years. Tamamo is not a limited servant and can spook you at any time. You could just wait for this to happen. Of course she may never spook you. I consider this the worst option but it is the cheapest sq wise.
I think the smartest choice is to get Tamamo first (option C) and build an arts team around her including Nero during Nerofest.
I would do that myself but Nero is a favorite of mine, I have several Tamamo supports, and I have a LARGE stockpile of sq (over 750 if you count tickets as 3sq) so I am doing option B myself.