40 years ago, when I was traveling regularly on business, usually flying, initially, I'd check my larger bag and have only my brief case full of 'business stuff' which included a reel of computer tape to match the one in my checked baggage. I always had a spare as I was installing software I had written on clients computers. On a trip to LA, my suitcase arrived the next day. That was it. Whenever I had to travel with a larger-than-carry-on suitcase, I'd ship the business stuff a day or two earlier via UPS. After a while, I found a huge garment bag with wheels on it! I learned to pack it all in that plus my briefcase. I could pack 3 suits & 5 white shirts along with underwear, etc in that garment bag! That was in the days before 20-30 seater turbo prop puddle jumpers, and I usually flew into major cities. So the size of the garment bag was never challenged.
These days, I can put a weeks' worth of casual (vacation) clothing, underwear and a bit more in an airline-size 4-wheel rolling carry on case. Everything else goes in a big gym bag I put on top. The advantage of the carry-on-size bag is that it fits perfectly under the seats in all Viewliner and Superliner sleepers, once I've taken out the hanging stuff and it 'deflates' to its minimum thickness.
As far as using the downstairs luggage racks, I've used them when I had to change roomettes enroute due to a late booking, and that way the SCA could make my old room ready for the next passenger and then flip my 'new' room for me shortly after leaving ALP...and repeated the process at DAL. I think the luggage is generally quite safe. However...I'd definitely not only put a well-secured baggage tag on anything there, I'd also add a TSA-approved lock, too. Putting a wrap or two of colored tape on the handle will also clearly identify it as your bag vs someone else with an identical bag.
Also, I would definitely avoid the 'super giant' size rolling bags. First and foremost, they often end up being too heavy to lift to the luggage rack about 4' off the floor. That limits it to being on the floor area of the bag storage area with other too-big bags. Riding coach, there would likely be quite a few 'too big' bags on the floor, too. I saw one lady bring a collapsible kiddie play pen and 'hog' about 50% of the total storage area floor space! Being in a sleeper, it didn't cause too many problems, but I did see a couple of 'monster' bags in the vestibule that the SCA had to move to the opposite side whenever the platform would be on the 'wrong' side. I think that was on the Coast Starlight, as I recall.
So whether you check your bag or not, do whatever works best for you. As mentioned by one of the prior respondents in this thread, if you check 'em, make sure you have at least your medications and other things you'll need enroute...or for the first day at your destination, too!
As a note for those reading that plan to travel in a Viewliner roomette sometime. There is NO auxiliary baggage storage area in a Viewliner. This past week, on a trip to New Orleans on the Crescent, across the hall from me were two 'newbies'...a 300 pound 'father', I think, and a 275 pound 'son'. Between them, they had a one-size-smaller-than-super-giant rolling case, a 'medium' rolling case, an airline carry on size rolling case, and an over the shoulder gym bag. I think they managed to get the carry on size and the gym bag in the cubby above the hallway accessible only in their roomette. The medium case apparently went on the 'shelf' alongside the bed where the hanging items would be placed. A few minutes after departure, I happened to observe them closing the door for privacy, and the big roll on case filled all or very close to all available floor space between the toilet, door, trash receptacle and bed. Once the lower bed was made up, there would be ZERO floor space!