Typically the only hoses which need to be special (rather, something other than just rubber) are fuel lines. These are usually reinforced with some form of fiber, like a polyamid (nylon) or sometimes steel or other metal mesh to increase their structural integrity. Fuel lines are generally under considerable pressure. Fuel lines also have special rubber in them which will not break down in the presence of fuel.
Coolant lines are also usually reinforced though more commonly only with a flexible fiber of some sort or sometimes just thicker rubber. Upper operation temperatures for an automobile's coolant system can, on some models, exceed 230 degrees. This puts the coolant under considerable pressure (as it remains a liquid at these temperatures), which the hoses need to withstand.
The only hoses which are typically un-reinforced are vacuum lines of various diameters. Evap system lines can be large outer (and inner) diameter, but are generally not reinforced.
Using a fuel grade hose for coolant is usually ok, using a coolant grade hose for vacuum and emissions is generally ok. Going the other way can get you in trouble, from a burst coolant hose, to an engine fire from fuel spraying around your engine bay due to a burst fuel supply line.
Beyond the considerations for material and pressure above, the only important factor in a hose is the inner diameter (so it fits over the fittings properly) and the wall thickness (usually only a concern on vacuum lines). A hose with too thin of a wall may collapse under vacuum and not perform properly as a result.
Hoses can be found at your local auto-parts store, but I prefer to shop on amazon, as the guy at the local auto-parts store may tell you that "sure this will work for X liquid" without actually knowing or looking.
The best place to get hoses is from the dealer, if it's in your budget. These hoses will come factory-fresh, and be pre-formed to exactly the right size and shape for each exact hose. You can search google for "OEM Parts" and find dealers which do a booming business in internet sales at a very low markup. In my experience (mitsubishi) I can order from a dealer in 5 states over, and get it shipped to my house for a third of what my local "stealership" would charge me for the exact same dealer part. The only concern is that internet parts departments tend not to be patient with helping you find a part. It's best if you have the part numbers before you shop with them.
Additionally, your engine gets hot and cold. The entire engine bay has thermal cycles as a result of this.
Worm drive clamps are easily the worst kind of clamp and fall into a group of clamps that could be termed as "constant size" clamps. With the exception of a compression fitting (another type of constant size clamp) constant size clamps should only be used on tubing systems where there is expected to be little to no fluctuation in temperature.
Constant size clamps will cause the hose material to be compressed by it's own expansion when heated, and will "squeeze out" around the clamp when warm. When the hose cools, this will eventually leave a gap between the extruded hose end and the fitting and the vehicle will develop a "cold start leak" which may seal as the vehicle warms.
It's usually wisest to use those "cheapo looking" spring clamps, if you can get the correct sizes. The are generally easier to install than to remove. These fall into a class which could be termed as "constant pressure", meaning the keep a constant clamping force on the end of the hose. The dealer is the easiest place to find the right size, but likely most expensive. I've had good luck with getting various sizes from Grainger. You need to measure the OD of the hose when it's installed on the fitting, and the max size of the clamp needs to be large enough to fit over barb on the fitting with the hose installed, but the minimum size of the clamp needs to be larger than the hose after the barb. There are other types of worm-drive-like constant pressure clamps, but they are very expensive, generally.
Another solution I've used recently on a motorcycle (where worm drive clamps were factory, ugg) are the Gates PowerGrip. You need a heat gun, but these clamps work great and have a wide range of sizes they will adjust. They are likely to be at least somewhat more expensive than getting spring clamps from the dealer, depending what sizes you need, but they are very reliable, are self tightening, and very easy to use (both installing and removing). They also make a tool to remove them, but careful use of a utility knife makes short work of them without damaging the hose.