I can speak from experience that installing an ion exchange softener is one of the best home improvements that I made.

I no longer need to explain to guests that 'yes the drinking glasses are clean, it's just the hard water'. I'm in Maryland and the first two winters here caused my skin to dry out, scratch, and crack mercilessly. Guess what? It wasn't the winter air so much as it was my hard water drying my skin (along with the lower winter humidity). Wife loves the soft water, say her hair is softer and has more bounce. What else? Oh yeah, those grey dingy toilet stains that I could never scrub off disappeared after about 4 months of softened water, the 10 year old bowels look as bright as the ones at home depot.

Now to your questions:
Skip the DIY water tests. Get a local lab to test the water ($50 here in the MD/DC area). Any installer is going to want to know hardness, PH, dissolved solids (turbidity), iron, and maybe manganese. The installer will run the tests, but having your own set will help with evaluating the system recommendations.

Can't recommend a solution without knowing a results of aforementioned tests along with daily water usage and service flow rate needed.

If you use an ion exchange softener it will, by design, supply water with zero hardness until the resin bed exchange capacity is exhausted. At which time it will then be recharged typically using nacl or kcl. Will it result in the saopy/slimy feeling on your skin - probably. But I love it! Remember, the squeaky clean feeling that your currently experiencing is actually the effect of the hardness in your water affecting how your skin feels.

What remington said, with a couple of exceptions/additions:

Dissolved solids is not the same thing as turbidity. Turbidity is a measurement of clarity and is caused by suspended (non-dissolved) solids and colloidal materials.

You want test results from an independent lab to get ACCURATE numbers. The sales folks that come to your house from the various vendors will use field tests that can be very accurate in the right hands. However, most of those folks use poor technique at best and will be well off the actual numbers. You city water report can be a good resource for you as well. Be aware that the water can pick up a few things on its way to your home, particularly iron which makes a huge difference when specifying a softener.

You want to know: pH, TDS (total dissolved solids), iron, manganese, chlorine/chloramine (I assumed city water based on your description), hardness, alkalinity, particulates (if you have them in your water you want to know amount and type).

Does your water have an objectionable odor or color?
Do you see rust-colored staining in toilets, showers, sinks?

You do not want to water your yard with sodium-softened water. Your grass/plants will not thank you for it. This leaves you two options. 1) As you mentioned, plumb to your outdoor faucets with untreated water, 2) regenerate your softener with KCl (potassium chloride) rather than NaCl (sodium chloride). KCl is more expensive, plus you will be treating alot more water. If you have a way to determine how much water you use indoors vs your total water bill, we can give you an idea what the cost difference would be.

Water softener providers:
Kinetico, as you mentioned, is good. They do tend to be the most expensive option. Their equipment is reliable, sales people are generally well-trained, and they do not require electricity.

Other national vendors such as Culligan are good. They sell reliable equipment, but sales people are generally less well trained.

Local vendors are well worth your time. Their prices are typically good and they have access to the same reliable equipment (Fleck valves) as the big guys, but often with more personal attention and better prices.

Once you have test results and a few vendor quotes, we can help ensure you get a correctly sized softener if we know the following:

1. Test results
2. # of people in the home
3. # of bathrooms
4. Any high-water-use items such as pools, jacuzzi tubs, mult-head showers?
5. Frequent guests?

There are a few things that you want:

1. 10% crosslinked resin (to resist chlorine)
2. gravel under-bed
3. top basket
4. USA-made resin (higher quality and better size control)
5. fine-mesh resin IF you have iron, standard if no iron
6. Fleck valve or equivalent
7. Anyone who gives you a quote should perform tests.
8. If a vendor is not responsive before the sale, they will be less so afterward.