Fragility: Double basses are not typically just falling apart the second you look at them. I had one do that, but there were a lot of other factors involved. A brief rundown of the fairly common concerns:
Let it live in your climate for a year: This is especially important with cheaper instruments not because of the bass being fragile, but because you want to be sure that it is well built. While you will likely encounter them on ebay for sure, even reputable shops that were trying to find something on the lower end of the market were buying really cheap instruments out of Asia, and many of them were coming from furniture companies that decided making instruments was a better economic idea. As such, many of those instruments were poorly constructed with wood that was not aged properly and while it might seem fine in the shop, within a year or so they started to fall apart. If it has lived in the shop for a year and not experienced those issues, or it did and the shop has fixed those issues, then you are safer than purchasing a brand new instrument and taking your chances that it will be ok. You typically can avoid a lot of that by purchasing from a violin family/bass shop as they tend to stand behind their instruments much more than a music store, but if you really feel the need to buy a double bass from Guitar Center, I would be really weary if it had a 2016 label in it. What are the issues you are trying to avoid?
Open seams: This is the most common issue/concern for double basses when they are exposed to changes in humidity. Essentially the instrument shrinks in low humidity and expands in high humidity. Hide glue is used because it was used traditionally, but also because we want to be able to take the instrument apart and put it back together again for repair purposes. If the bass has a big humidity shock sometimes a seam will open up as everything shifts, which could sort of be viewed as a fail safe; having a seam open is a more desirable outcome than a crack. If that ever happens, a trip to the shop with a bit of glue a few clamps, and some drying time takes care of an open seam, and your instrument is no different than it was before.
Cracks: A fairly common adage when it comes to double basses is that there are two types of basses; basses with cracks, and basses that haven't cracked yet. Most of the old Italian/English/other European countries' basses that have been around for hundreds of years have seen plenty of cracks, and they're still going. You want to avoid them in a newer instrument, and if the crack goes through the area where the soundpost is located on the top or the back, or along the bass bar on the top, they are costly to repair. If your instrument lives in your climate for a year or so and hasn't cracked, then there is a good possibility that it will be relatively ok. If you are bringing an instrument from a significantly different climate to yours, sometimes during the first month or two of that transition, or the first winter/summer when it experiences climate extremes, they crack. If it is a particularly bad one, located at the soundpost or bass bar, or on a cheap BSO, then you could have a situation where the cost of repairing the crack is more than the cost of the instrument, which is part of the reason why it is recommended that those instruments live in your climate for a year. If you maintain a relatively consistent humidity level year round you can reduce the risk of a crack happening, but there are basses that have lived in places with no climate control for years and survived just fine, and basses that have been babied from day one that happen to crack. It's part of owning this type of instrument but if they are repaired well, cracks aren't typically a huge issue.
Sunken tops: This is a particular concern on BSO's and cheap instruments. If they are not properly made, the top can sink. What that means is that the tension and pressure from the bridge pushes on the arch of the top of the instrument, and instead of standing up to it, the top "sinks" and becomes flat in that area. It is easiest to notice around the edges of the f holes. On a healthy top, both sides of the f holes will be on the same plane in the arch. On a sunken top, the outside edge of the f hole appears higher, because the middle of the instrument has been compressed. This is one of the "imploding" issues with cheap instruments, and you can't economically do much about it. On more expensive instruments it shouldn't be an issue, and if it is there are ways to correct it and reinforce the top, but it is a costly repair. Again, if the instrument survives the first year at tension without sinking then there is a good chance it will survive a few more, but that isn't always the case. If the soundpost falls, it is important to loosen the strings and remove the tension from the top to prevent this from happening.
Dings, scratches, etc.: Double basses are large. Regardless to how careful you are, sometimes you catch a door frame or something else unintentionally, and accidents happen. Some of those issues you live with, others you can have repaired. I purchased a new instrument and can still vividly remember the first traumatic experience when the finished was scratched. It involved my private teacher and a fork, and it took a long time for me to let that one go. Since then, even when taking very good care of the instrument, things happen. On older instruments, they call that "character". If the bass does not come with them already on it, most shops make "bumpers" for the treble edge of the instrument. They attach to the ribs and sit just slightly proud of the edge of the instrument so when you set it down on its side, the instrument rests on the bumpers and not on the floor, protecting the edge. It's a bit unreasonable to expect that your bass will never have anything happen to it, but they aren't falling apart all over the place.
Electric Uprights: These are another can of worms, and there is a separate section where they are discussed. The Coles notes version is that there are some that are very similar to electric basses and some that are closer to double basses in dimensions and neck shape/feel, but they are yet another fundamentally different instrument than double bass or electric bass. If I was going to make a guitar analogy, I would say that a double bass is an acoustic guitar, an electric bass is an electric guitar, and an EUB is a nylon string acoustic with a pickup in it. You can play "guitar" on all three much the same as you can play "bass" on all three, but they are different tools that can be more or less appropriate depending on the setting. EUB's shine in Latin jazz settings, but if you are working with a group that is looking for a "traditional" combo, they are not accepted in some jazz situations. They aren't taken seriously in classical music and you would never play one in an orchestra, but some of the ones designed with the bow in mind do have possibilities. I do not personally own one largely because the models I have played that I would be interested in owning aren't the cheap ones, but if you want to play double bass, the best instrument for the job is a double bass.
As far as brands go, it is mentioned in the beginner FAQ and other places that "brands" don't really mean as much in the double bass world. Shen tends to be one of the exceptions, because they are very consistent at producing good quality ply and hybrid basses at an affordable price. They have a dealer locator on their website that should help you out. Otherwise, you are best trying a bunch of instruments from a good shop, or if you are considering a private sale having the instrument looked at by a luthier to see if they notice any concerns that you did not before purchasing. Renting is also a great option if you aren't 100% committed to this yet, and depending on the shop, they may have a rent to own type program that you could take advantage of as well.
That's enough rambling for today. Happy hunting!