Best options for Luggage and Day Bag?

Use the search function. This subject is frequently, if not daily, discussed with few firm conclusion. It is probably split between wheels and no wheels -- so personal preference. I personally prefer no wheels as they only weight to the bag. But - if using wheels -- the large two wheels bags are superior for getting over rough terrain than the tiny four wheel spinners. And two wheel by design are subject to less damage.

Some will promote high end, big name bags but I find the $50 at Ross, or other discount place to be just as durable and functional. I prefer the bag with a zipper top over the clam shell. Some rooms in Europe are so small that is hard to find a place to open a clam shell bag. When shopping for a bag take along a tape measure so that you truly measure the size including handle and wheels. Generally the bag measurement on the tag is only the measurement of the bag itself.

I don't what you mean by a well designed day bag. Our day bag is just an old, scruffy book bag that looks unimpressive by design.

When carrying tech equip, along with general supplies, thought there may be bags that offer advantages, by design.

As far as day bag your first decision is crossbody or backpack?

If backpack, then if your luggage is also a backpack how will you carry both on travel days? Putting the daypack in the luggage may be possible if you go light. I've also seen some people carry the daypack like a handbag while wearing a luggage backpack, which to me defeats the whole hands-free thing, but it might work ok. If you have wheeled luggage this isn't a concern.

I prefer a crossbody (messenger style, or could be a purse for women) bag, but you will get a variety of opinions on that. My reasoning is the above (can carry it AND backpack luggage easily). Also I find it easier to keep an eye and hand on if I'm worried about theft. I like the look better, too. Finally, my biggest reason but not one that applies to everyone, is my camera. I carry a decent size SLR camera and hate stopping to get it out of a backpack every 10 feet. I also hate the look and feel of a camera strap on neck (heavy, painful, looks ridiculous to me). So I put my camera in a messenger bag in front of me and can grab it without stopping or doing the whole backpack removal dance.

My husband takes a video camera with different batteries and other equipment and uses this as his day bag, as he can also put personal items in it and it expands:
https://www.amazon.com/Lowepro-Passport-Sling-III-Protective/dp/B00J938IWG/ref=sr_1_9?ie=UTF8&qid=1531409256&sr=8-9&keywords=sling+camera+bag

For suitcases we both take a 20inch Samsonite Fierro hard-shell case. We also each take a personal item, hubby a backpack (Used for plane and train) and I take the Kipling Sherpa Bag (For plane and train) and for a day bag I use a cross body light weight purse with a top zipper. We travel by train only and found this combination is perfect for us. We usually travel for 15 -21 days.

This is my backpack ( fits under seat on airplanes) and just lightly filled for day touring pack

http://www.eddiebauer.com/product/stowaway-packable-20l-daypack/82300168?showProducts=&color=147&sizetype=&size=

My main bag is a 21" Travelpro, similar to this one ( this is a current model of my 5year old bag)

https://www.ebags.com/hproduct/travelpro/max-lite-4-international-carry-on-rollaboard/311978?productid=10417655&cat=carry-on-luggage&country=US&currency=USD&sourceid=ADWPRODUCT&adtype=pla&gclid=EAIaIQobChMI6tj6pLya3AIVj1uGCh3MewYQEAQYAiABEgK9rvD_BwE

Easily did 4 weeks with these

Here are some tips.
Daypack size: 15 liter - 20 liter
Luggage Size: About 40 liters
Good Combo.s
1). Two-wheel rolling case and daypack.
2). 40 liter backpack and a packable stowaway backpack. (Folds into pouch)
Carry-on luggage size: 20"-22" x 14 x 9"
Get a small combination luggage lock to use on suitcase/backpack and daypack.

Have you looked in your own closet and those of your friends/relatives to see what travel bags are available? Not necessary to have all-new, highest-tech -- and what's optimal for one person can be horrible for another.