Traveling with a guitar is tricky. The airlines tend to toss baggage around like there is nothing valuable or fragile in there. I have hard shell cases and I also have a gig bag, made by Superior. I think they make the most convenient and well thought out gig bag. And they go for about $40. Well worth it. My dreadnaught also fits readily in every overhead, so the guitar can be carried on. The down side is if they won't let you carry it on. And in this climate of fear as a political tool by the present regime this is a possibility. So it's best just to have a good case, wrap the guitar neck with something (bubble wrap is good) and put it in a hardshell case. Usually a good guitar will come with a good case. As of this writing, all of the airlines will allow you to carry a guitar on to the flight and put it in the overhead, unless you are traveling in a puddle jumper that will not accommodate anything thicker than a valise
As a rule of thumb, always be polite and considerate of the flight attendants and ticket takers, as they can frequently make the call to put your guitar into one of their closets or behind the last row seat or something. If you make a stink or carry an attitude then there is a good chance that they won’t help you. It is not their rules and they do have superiors to answer to, so just try to be as nice and understanding as you can be and do everything you can think of to get them on your side, short of washing their pets.
A final option is to do what they call “gate check” . This is when you carry the guitar all the way down the jetway and then one of the baggage handlers takes it from you and carries it down to the hold of the plane. Upon landing, they take the gate check items and bring them back up to the jetway and you can pick up your guitar as soon as you step off the plane onto the jetway. In this way, you at least avoid the baggage handling machine that could easily grind up your guitar. Many professionals and amateurs also carry a traveling guitar. Taylor makes one called the Baby Taylor and so does Martin. They sound good, and play well, tho they aren’t like dreadnaughts.
As to brands of guitars, there really are many good brands. The Eagles travel with Takamine acoustic/electrics. They work and sound great. I travel with the Collings or the Taylor. The Martin D-28 herringbone, I keep in my bedroom and play every night. I always wanted that guitar and found a good buy on ebay, so I went for it. You can find a good guitar on ebay, but you have to know what you are looking for and what you are buying. Don't do it unless you have someone knowledgeable working with you. Initially, I think it is better to buy from a dealer. That way you have someone to talk to, work with, and complain to should such a need arise. Developing a relationship with a dealer also puts you in the loop when something new or something you specifically want comes into the store. They can call you and tell you that a certain guitar just came in on consignment and they can help you negotiate a fair price. It's always better to reach a fair price. One you are happy paying and the other fellow is happy receiving. Then you have another relationship to which you can refer or employ.