There are a few things in life one shouldn't DIY & this is one of them. Of course if you wish to ignore that & move ahead it all starts with a full Manual J, S, T & D. Once you have that done properly, you will know what equipment & ducts (unless you go with a ductless mini split) you need to get. The manufacturers all provide step by step directions so you should be good to go. (well with the right tools, etc...)
Sizing the load and the ducts can be done through several web sites that offer this service. Often called Manual J and D. You can also purchase the duct supplies at your local big box stores. Where your going to run into issues is the equipment side of things. You cannot purchase legally any cooling equipment unless you hold a certification in refrigerant handling. As the systems come partly charged. Also prepping the refrigeration pipes, evacuation of them, silver soldering them while using nitrogen all takes special tools that most home owners do not own and cannot rent. In addition many of the supplies needed may not be able to obtain as many of the suppliers of HVAC equipment only sell to contractors in this field.
What I would suggest is that you contact a few local HVAC contractors who are willing and who would possibly size your system for you, and provide you with the information needed to install the air supply and return system. Once that is done, then contract with them to install the equipment to your self installed duct system.
Installing a duct system is not all that hard, it does take a few tricks to make it go faster and having some proper tools make it much easier, but if your looking to save a few dollars you can install some of the ducts yourself.
In the past I have had a few clients install their own registers and flex ducts. We sized the flex and grills as well as locations for the install. Once done we then fabricated the main duct runs and installed the equipment for them. Saved them a few hundred dollars.
But SLS Construction Solutions is correct, this is not normally the best type of job for the DIY person.
Just a suggestion you may want to consider. Now there are ductless A/C and/or central heat and air products.Very new and not advertised. Have seen this on HGTV many, many times. I called several companies in my area and some were helpful and others were not. You have 3 choices to choose from; low end, middle end and high end. You can bargain with these folks and get discounts and factory rebates of $200.00 and more. The mid-range price for one unit was $3300 to $3400 and 2 units was $5000. All this depends on the size of your home.Warranty was 6 years for compressor and 2 years on parts. Plus these units are VERY energy efficient. Now, this was from just one company that I called. Just so you know.