I came to this too late, looks like you went to an urban, well-heeled suburban or hotel based high-end steak house, but some ideas for the future....
I have not done many fine dining shops, but I worked fine dining for years after starting in family and business restaurants and I dined well for years. My husband got upset that I would not join him again for a couple of big region wine tastings for the trade this week to celebrate my birthday, but I always worry about the kids after school staying on task for my mom.
If fine dining, which I think is loosely defined for shop purposes and as the restaurant industry has evolved, my instinct as shopper experiencing or bartender or captain serving (a phrase used for true fine dining with a layered service team) ...GET A RECOMMENDATION! That is what these people are there for, not to take orders. Go to a kiosk restaurant if you want an order taker. It can vary based on your preferences but use this opportunity to get out of your comfort zone. If there are specials, you should not ask, they should offer, they should ask general questions about preferences, but they should sound you out and open up your mind, They should describe flavors. Don't necessarily go with what is popular. That being said, keep it light or simple, why spoil your palate with something heavy. And the shop requirements may dictate a cocktail. Even within that constraint, there are options this location should have, even if it is an update on an old classic. Or get a spritzer, a simple aperitif, or a very dry something...fino sherry is not for everyone nor readily available, but something low acid, subtle.
At the table, if this is truly fine dining, these restaurants do not typically have house wines. I think of higher volume or mid-scale chains for that. You will more likely, even if modest, have a selection of wines by the glass. There could also be half bottles. Your waiter/captain can and should assist, But even if you want a simple glass or two of wine, stay away from the obvious. You will always get better value and better pricing on the less obvious varietals or proprietary blends (this basically means it is an odd mix of blended grapes that do not fit into a classic category, like strictly Rhone varietals or Bordeaux blends) or regions whether or not there is a global selection--think Spain, South America, Oregon, select Michigan or New York wines. Yes, I like my single vineyard Chardonnays or rustic and Grand Cru Burgundies, I love first and second growth Bordeauxs. etc.but there are wines out there that do not cost a lot and can transform a dining experience with the right match, even if you would not normally drink it. Chenin Blanc or Riesling with a BYOB Thai restaurant stands up well to heat and sweet and spice even if you think you would only drink red wine.
In other words, stay away from Kim Crawford Sauvignon Blanc, but if they have valet, I do not think it is an issue.
I have eaten in plenty of hole in the wall restaurants in Chicago and New York and elsewhere with solid food, knowledgeable service, and great wine recommendations. I even like to know what someone thinks of it if they have had it before or if I am torn between a couple of options, which could work best and why.
I recognize that all of this may not apply to your situation. You must blend as a regular customer, and I worked plenty of New Year's and Valentine's Days and anniversaries with the amateur diners, those that may go somewhere special outside of their budget to celebrate or because they had babysitters, etc. I now count myself as among that group...but my husband works all of those holidays. So do not worry about not blending in with the more typical clientele demographic. Even if you are not expert in any of this, good hospitality is good hospitality in any service experience--engaged, friendly, helpful, accommodating.
And that Chardonnay thing, stay away from California as a rule. Chateau Montelena from northern CA is a classic unoaked Burgundian style, if offered usually by the bottle only and is a very good value if someone really wanted a Chard. Oaky, buttery CA Chardonnays are generally...not worth it. That buttery, fat, flat quality is a product of a secondary fermentation called malolactic. They all taste the same after awhile. There is more to life.