Got married in 2015 and we was in the same boat as you... Both of us are from large ethnic families who wanted to give physical gifts (because they're well intentioned and wanted to pay it forward - a lot of them were newly arrived in the US without a lot of money, and sometimes not a lot of family and married pretty young - so gifts they got for their marriage were actually very much needed). Both my partner and I already had functioning apartments (separately), then when we moved in while we were engaged, realized we had about 2 of everything and had to narrow that down. Thankfully, we are pretty minimal people - him by nature, me by intention. But especially after having to sort through both of our belonging to weed out duplicates, we really felt like we did not need anything else.

We ended up taking a two pronged appraoch: 1) Upgrading things we had, and used, but that were not all that nice to begin with and 2) Items that would help us achieve the goals that we had laid out for our relationship as a married couple.

A few things we asked for that have seen a lot of use:

1. Vitamix - I thought this was going to be a huge waste of money, but my partner really wanted it and my aunt really wanted to give it to us (because she loves hers). This thing has gotten used daily (and sometimes multiple times a day). We have been low-carb-ish for the last two years and the Vitamix has been awesome for this kind of cooking. Can't say enough great things about it and I have no doubt this thing is going to last decades.
   
   
2. Really great Japanese knives - my cousin is a chef recommended this pearing knife and this 8.5" knife. Not only are they super easy to handle (as opposed to German Wostoff knives - a commonly requested wedding gift, which IMHO are way too large to efficently or precisely manuver), but they are gorgeous knives that are nicely balanced and really feel great in your hand. We replaced an entire block of cheap-o knives with these two knives alone.
   
   
3. Religious & ethnic items for holidays - There are a few holidays we celebrate where specific items are part of the tradition. For example, for Christmas, our families always have nativity sets, so we registered for that. For Easter, there are special cultural items that are used - and someone made us that. You can ask your ethnic families to get you these things (which were actually some of the most touching gifts because they were either made by hand or purchased overseas).
   
   
4. Plates, silverware, glasses and servingware to host 40 people - This is NOT "minimalist" for pretty much anyone, but it made sense for us. We both have large families. The elders of the families have been strongly hinting at having us take over the "big holidays" that they have been hosting. Additionally, we live in a neighborhood that is the spot for 4th of July parties, and we host an annual blowout day-before-Thanksgiving party. When we were making our registry, we made a list of everyone who would be on the invite for these parties and were hitting the 35-40 person range. So we have 40 place settings - we keep 32 of them in a separate set of cabinets in the basement, and 5-6 times a year, bring them out so that everyone can eat together using real plates and silverware. It's not minimalist, but it's intentional in that we specifically have choosen to stay in the same city as our families so we can do these types of things.
   
   I guess my overall advice would be to make a list of goals you want to achieve for your life together, and then try to ask for items that either help you achieve those goals, or enhance those experiences.
   
   A few examples:
   
   

• If a goal for your married life together is to be environmentally sustainable, think about registering for a compost bin, a fancy SimpleHuman garbage/recyling can or a Berkey Water Filter
  
  
• If you want to pursue a healthy lifestyle together and cook homemade meals - you can upgrade your pots and pans (love my All Clad pots and my Le Creuset pan).
  
  Does anyone NEED this stuff? No, of course not. But when you're lucky enough to already have all your basic needs met in life, wedding registries provide are a nice opportunity to upgrade things that were aquired at an earlier time in your time in your life, not for their enduring quality, but rather their low cost/ ease of procurement. Good luck!

https://smile.amazon.com/gp/product/B00B4UOTBQ/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

It's not cheap, but I've had it for years and it's pretty indestructible. It's not the thin chemical non-stick coating, it's the cast iron covered in black enamel. I've put it in the oven, on the grill, in the dishwasher, it's been dropped, scraped and burned, and there's absolutely nothing wrong with it.

It’s totally non-stick if you’re cooking meat, but you’ll need to use plenty of fat if you’re cooking eggs.

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Edit to add description in case link doesn't work:

Le Creuset Signature Iron Handle Skillet, 11-3/4-Inch, Cerise (Cherry Red)

A skillet is just a frying pan. In the US they use skillet, frying pan and fry pan pretty interchangeably. In the UK we often use skillet for non enamelled cast iron frying pans as they will likely have been imported from the USA (or were made for the US market, or were inspired by it) so keep the name, e.g., "Lodge 26.04 cm / 10.25 inch Cast Iron Round Skillet/Frying Pan" on Amazon UK is made in the USA so keeps the name.

I mentioned "non enamelled" because we still call Le Creuset enamelled ones frying pans here even though they are skillets in the US, e.g.,

Le Creuset Signature Iron Handle Skillet (Amazon US) vs CAST IRON FRYING PAN (Le Creuset UK).

A "cast iron griddle pan" is just a "cast iron griddle pan" or maybe "grill pan" if you prefer. It's a frying pan with ridges.

Le Creuset Signature Iron Handle Skillet
https://www.amazon.com/Creuset-Signature-Handle-Skillet-4-Inch/dp/B00B4UOTBQ/ref=sr_1_fkmr2_1?ie=UTF8&qid=1487420830&sr=8-1-fkmr2&keywords=Le+Creuset+Cast+Iron+Skillet+Pan%2C+23+cm+-+Cerise

I know you're asking which of the two options to keep (and my answer is the stainless, because as much as I love cast-iron, if I had to only use one for the rest of my life, the stainless is more versatile), but to consider for the future: you can buy enameled cast iron skillets! Cuisinart, Lodge, Tramontina, and Le Creuset all have them. Both the exterior as well as the interior cooking surface is enameled on all of these, even though it doesn't look like it in the photos.

Edit: I suck at formatting.