Mostly it would be very light projects. Other than shop class many years ago where I did a little stick welding I have little experance with welders.
What would be the best type of welder for home/farm use? I know there are several basic type like the AC/DC, Flux wire, Gas wire.
Which in long term be least expensive to operate considering welding supplies, electric use, etc.
What brands should be considered?
Any other must haves? Welding hood, gloves, grinders....[/QUOTE]
The best welder for home/farm use is the one you can weld the best with. You have some experience with stick welders so that would be the one I would start with. If I could only have one welder, for the things that I like to weld (mostly 3/16" and thicker steel), trailer hitches/wood stoves/ trailer frames, motorcycle rails, stuff like that, my choice would be a stick welder. I like to weld outside whenever possible. A friend of mine lost his almost new shop/garage to a smoldering welding spark. When I weld outside I don't have to worry about it. Since wire welders don't play well with wind it limits where they can be used.
The stick welder will work with electrodes that have been impropperly cared for (most home shops don't have climate controlled rod storage). The last 50 lb box of 7014 I bought has been sitting open on top of my welder for the last 15 or 20 years. It still does what I need it to do, farm welding.
If I leave a spool of wire sit in the same location it developes rust on the surface and doesn't feed or melt correctly because the rust insulates it from the liner of the wire welder feed cable. In Michigan we get a lot of moisture in our unheated buildings do to the drastic temperature changes. It is not kind to wire over the long term.

To prolong its useful life I have to remove the spool from the wire welder and store it in the house when it is not being used. A little inconvenient but it helps.
For thin sheet metal the wire welder wins hands down.
I have both kinds, a 160 amp Clarke 220 volt wire welder that can be used with gas or flux core and I have had 3 Stick welders. My first was an old 225 amp copper wound induction cooled Westinghouse with a crank style power setting, I sold it to a friend about 25 years ago, he is still using it. I then bought a used Montgomery Wards 250 amp AC/DC with a slide type power setting. I just recently purchased another Montgomery Wards 295 amp AC only welder for $75 on Craigs list to use in one of my barns.
I had used one like it a couple weeks earlier at a friends house to weld some flanges on a 6 foot tiller I had bought, I was very impressed with the stability of the arc and the ease of starting.
These are all light duty consumer grade machines. They have serverd me well. I have burned up about 100 lbs of 7014 and about 50 lbs of 6011 and a small amount of nickle rod on cast iron. I have no complaints with any of them. I like the infinite power settings better than the "click" style that is used on some welders, it allows me to adjust the power to fit my welding style rather that having to adjust my welding to fit the available power. These old welders seem to never wear out and you can often find them in the $75-$100 price range.
I think the stick welders are a little cheaper to operate, but not by enough to make any real differnce, but if the cost is a concern then I think the stick welder will be your best choice if buying used.
As far as brands, I have only used Westinghouse/Montgomery Wards/Lincoln and a comercial 100% duty cycle Miller 250 amp AC/DC. They all work great.
I liked the auto darkening hood that I bought at Harbor Freight. It burned up in my barn fire so I am going to get another one. It make life a lot easier for those of us who don't weld frequently.