1. You likely aren't going to get the sound you are looking for on anything smaller than about 5/8ths, or a 39" string length, and that is if you find one of the few exceptions to the rule in that size. FIT as you call it is important, but unless you are a particularly petite individual with very small hands, you can achieve it on a "standard" 3/4 instrument with a 40-42" string length. If you have been through the beginners' guide and done some reading, you will have discovered that fractional sizes are largely open to interpretation, with 3/4 meaning anything that is a regular sized bass, 7/8, 4/4, and 5/4 are reserved for instruments that are atypically large, and 5/8 is for anything that is on the smaller end of typical. 1/2 and 1/4 size instruments are typically intended for young children, not only because they are shorter, but also because they have yet to develop the hand strength to play a larger instrument.
I personally have not the largest hands and play on a 41.5" string length and a large-ish 3/4 size instrument, and I know countless other bassists who are shorter/smaller people who manage a full size instrument absolutely fine. Slope of the shoulders, overstand, (the distance between the top of the bass and the fingerboard at the neck joint) neck angle, if the back is canted, if the ribs are tapered, how long the table of the instrument is, and a ton of other variables are at play when determining how a bass fits to a bassist. Depending on the type of music you are planning on playing, you may or may not require access to the end of the fingerboard and beyond, and if you do, there are plenty of basses out there built with soloists in mind to make it easier to get up there.
Fractional instruments tend to leave a lot to be desired in the sound/tone department, and you are needlessly limiting yourself by starting off your search with that in mind.
2. Depending on what you are going for, some jazz guys like to have a lower string height to achieve what you are looking for. On an electric you will experience fret noise if your string height is too low, and if you play really hard or bow really loudly on an instrument with low string height you can experience a similar situation on double bass. Typically the "jazz setup" that some guys go for is low string height and Thomastik-Infeld Spirocore Mittel strings which you can pair with a relatively hot pickup/lots of head room to give you the sound I believe you are looking for. There are a lot of other ways to achieve a desired tone besides just setup, and technique plays an extremely large part of that on double bass. It is also very easy for poor technique to lead to injury on double bass, so even a few lessons to start you on the right path, avoid bad habits, and show you some of the differences between electric and double bass, (they are fundamentally different instruments even if they do share a role and tuning) is a very good idea.
3. Technique again is a big part of tone. Carved tops tend to vibrate a little clearer because they are one piece of wood moving as one, not several competing with each other. They are ply basses out there that can sound great and they aren't a bad option for a first bass, but you can also get into a hybrid at a fairly reasonable price and there can be a significant difference between the two.
4. The Ebay/Amazon BSO's are called "Bass Shaped Objects" for a reason. Almost all of them are made out of inappropriate materials to make a double bass out of, and every possible corner is cut to try to keep the price down. When we talk about cracking/imploding, that tends to be the norm, not the exception. Many of them suffer from sunken tops which are an extremely costly repair on an instrument that is worth it, a lot of them have seams that open up, but they were put together with Titebond instead of hide glue, so shops refuse to go near them because they are impossible to get apart or back together again. Often the neck is set at the wrong angle, or it shifts because the mortise is poorly cut and then a ton of wood glue/filler is used to take up the slack, which falls apart under tension. None of those things are setup related, they are poor construction related. Think of the $900 double basses on the internet as a similar option to the electric guitars sold in a big box electronics store. It might be cheap, but you typically aren't getting something worth playing at Sears/Radio Shack. It would be akin to purchasing an electric bass where there was a significant chance the neck would warp, a few frets would fall out, the pickup likely isn't wired correctly, and the neck joint was carved out by a drunk with a grapefruit spoon. None of that can be fixed with a professional setup.
I haven't read the beginner guide in a while, but it likely suggests you start somewhere in the neighbourhood of $1500-2000 for a ply instrument, from a reputable violin family/bass specific shop instead of Sam Ash/Guitar Center. Most violin family/bass shops have explored a significant number of options to find an affordable instrument that meets their standards, and many of them set them up, put a better set of strings on them, and often fit a new bridge or endpin as well. This is why you can occasionally find the same brand/model of entry level instruments at a Music Store cheaper than at a bass shop, but often that doesn't include the work the bass shop puts into it before considering it saleable, and you will often spend more in the long run buying it "cheaper" but having to take it somewhere to have the setup done.
5. Generally, it is a good idea to purchase an instrument that has lived in your climate for about a year. I personally would only buy an instrument that hasn't lived in my climate for a year if I was commissioning an instrument or found a great opportunity to purchase a pedigree instrument. While accidents happen and sometimes problems take longer to become evident than others, if an instrument survived its first year through your local seasonal shifts, there is reason to believe it will survive longer than that. If it is brand new or brand new to your climate, then you run a higher risk of sunken tops, open seams, or any other plywood implosion experiences. Some shops don't even let an instrument on the floor until it has made it through its first year, although that is significantly easier to do with violins than basses, given how much less space they require. At the very least, most shops give the instruments a few weeks/months to get accustomed to their new home before doing setups and adjustments, if for no other reason that they don't want to do them a second time when the instrument settles.
If you purchase from a violin family/bass shop, typically they will tweak/adjust the setup for you if you know what you want done differently when purchasing the instrument, (a lot of them are set a little on the high side for the players that like that, and then they can lower them if necessary for someone else) and again in another month or two after you have lived with the instrument for a while and noticed you would like something a little different. That often involves changing the string height, adjusting the bridge and/or nut, or moving the sound post around a bit but if you want something more invasive done, that's up to you to pay for.
To sum things up, you more than likely don't want/need a small instrument for playability, sound, and tone reasons, Spiro Mittels are a great place to start for jazz strings, a carved top isn't required but you might find you like/want it, technique is a significant part of the sound/tone equation, BSO's are a bad idea, and a bass that has lived the local life a little will usually be happier there.
There are also a lot of fantastic older instruments out there, and "used" has far fewer negative connotations when it comes to double basses than most other purchases. All of the double basses with the biggest price tags also happen to be old, some of them a few hundred years. But this has already got really wordy and given you plenty to think about.