I would like to be able to make sorbet with whatever ingredients I have on hand without always looking up a recipe. I understand that it's important to get the correct balance of sugar, liquid, and other ingredients for the end product to have the right texture.  There seem to be a couple options for testing your sorbet mixture: syrup density meters and refractometers. Before I spend money on one of these tools, I'm wondering:   Can I reliably make sorbet without one of these tools? What techniques do you use to make sorbet with each of these tools? Are there advantages/disadvantages to one way or another? What do I need to know about the different scales (Brix, Baumé, specific gravity, other) and what readings should I target? Are there other things to consider regarding ingredients (purée v. juice, effect of additives such as alcohol, etc.)?  
Your question asks about a lot of very specific scientific detail, but really, with a bit of experience, you can make sorbet without any of that.  For most fruits, you need about 1/3 as much sugar as fruit by volume - two cups of fruit and 2/3 cup sugar is pretty common in recipes. This works with a good variety of fruits - for example, mangoes, strawberries, and kiwis should do well. If it's too thick, you may also want to add a bit of water, perhaps even up to the amount of sugar you used. With less water, you'll get a richer, more velvety, perhaps almost creamy sorbet, depending on the fruit; with more water it will of course be icier.  Of course, you'll end up adjusting the sugar sometimes - a bit less for very sweet ripe fruits, and a bit more for less sweet ones. But so much of the sugar is coming from what you add that you don't usually need huge adjustments; it should generally be somewhere in the 1:4 to 1:2 range. And there's enough variety just in the sweetness of the same fruit that predetermined ratios aren't always exactly right anyway.  If you make a few sorbets from recipes, you should be able to judge well by taste: before freezing, it will be quite sweet, a bit more than you'd want to eat. Unsurprisingly, it should be similar to the sweetness of melted sorbet, perhaps a bit more sweet than melted ice cream.  And as always, adding a shot of liquor will soften it up; this is handy if you find that sorbets softened only by sugar are too sweet for your tastes. Neutral things like vodka are handy since they'll work with any fruit, but sometimes this can also be a way to add an additional flavor. And if your fruit works with a wine - strawberry-rose and blackberry-cabernet are both pretty good - then using wine instead of water will soften it very nicely.  Finally, I noticed the juice vs puree point. I've never made sorbet with juice, but I suspect that'd be prone to being really icy. I've always used pureed fresh fruit; it'd have to be really good, fresh juice to taste as good as fresh fruit. 