I'm about tired of just having a window unit in one room, so I'm looking into either getting central AC or a mini split system installed.
I have central heat, but not AC.
The duct work needs redone as it is old and too small.
Been wondering which type of system would be best both in performance, and value to the home.
Oh, how is it best to go about getting a good contractor?
About all I have to go buy is reviews that are on the net.

I could refer someone very good to you if you are local. However I am in NC and do not know where you are.
I recently had to replace my ac/heatpump. I went to Angie's List and check the dealers listed. I made my choice from that.

I'd just get central, spring to get the duct work redone and I think you'll find it worth it.

-USAF HVAC tech.

My son-in-law got a Mitsubishi Split type after replacing a large 220v wall unit twice within five years. It's a very difficult LR-DR-KIT room to condition since our large family (35-40 people) gather there for occasions.

It's been used for about 4 years and been doing an amazing job at keeping it comfortable in there. It has a technology that produces widely variable cooling output so it magically ramps up and down to maintain the temp. and it is whisper quiet.

I have central AC at home, but the Mitsubishi does a better job at maintaining a uniform temp. in the space.

I have what sounds like the same Mitsubishi system as 'Zip's son-in-law in my Oregon place. It is great at both heating and cooling, and we got a $900 (?) rebate from the power company because is is so energy efficient.

These systems are also called ductless systems. Usually cooling pipes/hoses are run on the outside of the house, but in my case since I was remodelling anyway I had them built into the walls and run some inside under crown molding.

Whisper quiet and nice to be able to control temps room by room.

My Oregon place is only two bedrooms and about 1000 sq ft. I paid about $10K, installed. It works great and is quite cheap to run.

Don't you have to have a condenser and a wall unit for each room with a split?

The condenser unit (AKA heat pump, as I understand it) sits outside the house against an exterior wall. Each room, or area, has a thin wall mounted unit up near the ceiling. They operate by independent remote contros for each interior unit. In my Oregon place, I have one wall unit for the living room, kitchen, and entryway which make up the first floor, and, upstairs, one wall unit in each of the two bedrooms.

So if I want to control the temp in the entire house, I can turn them all on and just leave them on. If I only want to cool a bedroom I am in, say at night, I can turn the others off.

My house in Japan has an outside unit for each inside unit. (So in Japan, in an 1800 sq ft house, I have seven outside and seven inside units.) My house in Oregon has one outside unit for three inside units.

I think the one for one approach is cheaper, but the three for one approach certainly reduces clutter. My power bill in Oregon is a lot cheaper, too, but that surely has to do with respective power costs in the two countries as well.

You might find this helpful: Zoned Comfort Solutions™ | Mitsubishi Electric Cooling & Heating

Thanks for posting the link. I saw mentioned the wiz-bang tech my SIL was talking about. Sounds Buck Rogers-ish but works like a charm. No temperature hunting like at my house, where the central AC thermostat located in the hallway let's the rooms get too warm before it kicks on and then makes them too cold before it kicks off. Of course I then annoy my husband by accusing him of messing with the thermostat.

I'd trade for the Mitsu in a heartbeat.

I always get contractors from friends that have recommended them. If I am in someones home and admire the work that their Contractor did I will get the name & number - even if I don't need him immediately.

There is always a demand for top notch HVAC guys and I would recommend if you are serious about installing A/C that the best time to do it is in the "off-season" - if possible of course. Right now good Contractors are more likely up to their necks in work and you will pay top dollar "in-season".

I'd also use someone that did a friend's home that is very comfortable & has had trouble free climate control since installation. There are plenty of HVAC guys but only a handful of top notch ones. Check out the installation and see how the guys work is. Sometimes just a good look and a little common sense can help you asses work he has done in the past. For the better guys expect to pay for their expertise.

I installed a one condensing unit/ two ductless system in my garage apartment. It was dead easy (except for the ladder part when I ran the hi and low pressure copper). Here in high humidity Texas gulf coast, the only issue I hear of with the mini splits is the condensation lines get blocked with algea (or whatever that stuff is called) and walls get wet. I pour a little H2O2 in the drain pan every couple of months, but I never had that problem anyway.
My house was a different story, I have a large attic, so running new ductwork for the central a/c was easy and the new airhandler is smaller than the original one, so I stuck with central in the old hacienda.

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Halfway and one more step

Just for the heck of it might want to check with the power company.

Several years ago our power company was offering to replace or install new systems in older homes, then allowing customers to pay interest free with modest monthly payments that came with the power bill. A couple I talked to seemed pleased with everything including price. And they had a crazy long warranty IIRC.

Happy AC hunting.

Any ideas on what I'm going to have to spend on a roughly 1500 square foot house to get either type done?
Existing duct work is in the crawlspace, and the heater is in a sort of small basement, and is a 90% gas unit that is fairly new.

There are plenty of sites that can give numbers, but as has already been mentioned, there are numerous cost variables depending on your location and your utility company. Since you have not supplied your locale or power provider, this site gives a starting point to see what credits and rebates are available.

Tax Credits, Rebates & Savings | Department of Energy

Sometimes the higher initial price of a unit is offset by these incentives.

Never mind the A/C system, I just want five minutes in a room with the clown that under specified the attic insulation and designed in all the heat leaks in my current home. I'll be the guy carrying the baseball bat....

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Release the Kraken

I'm in Arkansas.
Provider is Entergy.

Arkansas and Federal rebates on AC are unavailable so far for 2017. Entergy is offering up to $1768 for heat pumps or $1336 for AC.
Requires qualifying unit and duct sealing and ECM motor to get the max rebate.

Entergy Arkansas - Residential Energy Efficiency Programs | Department of Energy