You'll get a lot of opinions on this but do some google searches.  Mig welding on thin sheet metal is difficult - constant cleaning, burn through, etc.  Gas welding with .024 wire works well with some practice.  I bought separate panels for my floor replacement and did them in sections.  With my limited welding skills I overlapped the panels with about 1/2" and used self tapping sheet metal screws to hold them in tight.  Since my car was on a rotisserie I did 1/2" stiches on top separated by 1/2" and then stitched the underside at the open areas on top - effectively giving me a full weld.  Once welded, I removed all of the sheet metal screws and plug welded those holes.  There is a chance that the overlap will allow moisture in someday, I painted it all with epoxy and applied liberal amounts of seam sealer on both sides.  Don't take any shortcuts.  If you have rust under the seat riser, remove the seat riser and plug weld it back in.  I have some pictures of my repairs that I can send via email if you send me a message with your email address.

You'll have a lot of labor hours in this and the cost of a welder that supports gas and can be used effectively on thin sheet metal is a small investment when looking at the total cost of the repair.  Gas yes, flux no.

Regardless of the weld method, you'll need to remove all dirt, oil, grease, paint, and rust in the areas that you intend to weld.  No weld method will work well if the parts aren't clean.  That includes on top and underneath.  Dirt on the bottom surface of the floor will spoil your welds on top.

Let me preface this by saying I learned to weld when I was about 14 on an ancient stick machine.  Using that as a frame of reference more modern types of welding seem super easy (no arc starting, etc.).

That said, IMO MIG welding sheet metal is easy (yes, I've successfully stick welded sheet metal).  In general its probably the simplest form of welding there is.  The machine will come with a guide that will give you your settings for amperage and wire speed based on the thickness of the material you are welding.  I can't say its completely idiot proof, but its about as close as it gets.  The only other variable would be wire thickness, but the guide will account for that as well.  For the sheet metal used in these older cars I would use 0.025" wire. 

Personally I would use shielding gas.  For steel you can use cheap gas (25% Argon 75% CO2, or possibly just straight CO2).  Flux core wire works, but its a lot more like stick welding.  You get a fair amount of spatter.  Its not very clean, whereas with gas there's basically no spatter.  Flux core welds also cool with slag on top which needs to be cleaned off.  There's no slag with shielded welding. 

Another thing I would advise is invest in an auto darkening helmet.  Its one less thing to have to learn technique wise. 

A good way to start is to find a local welding supply shop.  Even if you don't buy your machine from them (used ones will be cheaper but stick with a name brand like Lincoln or Miller) they can check it over for you and give you advice on what to use for what you're doing.  For sheet metal a small machine running on 110 is fine.  I can weld up to 1/4" material with my 110 machine.  That's going to be plenty for the average hobbyist. 
 

Doug, i have a Lincoln 140 mig that i use for sheet metal. I would definetely go with mig gas over flux core. As RPM said it takes more heat to use the flux core. More heat means more warpage and burn through. When you try to fill the burn holes, you get more heat and warpage. I have not seen a handheld laser that i would trust besides the professional models which are definelty out of the one car fix range. They cost more than the car would be worth. 

The only thing a flux core welder does better than shielding gas, is it's able to weld outside on a windy day.
It's not worth the disadvantages though.
 

Thanks all or the recommendations. I’ve been welding since I was a kid. I learned on Oxy/Acetylene and have mostly worked with thin sheet metal. When heavy duty welding was needed I did ARC welding. I played with wire fed welding many years ago long enough to see how it worked. Some guy set it up for me so I’ll need to learn how to do that. I don't remember if it used gas or not but I did like it. I want to do the welding in my garage with gas because of the less potential for sparks.

Couple-a question to axe of yourself......you plan on selling the car ?
                                                                does it have carpet and mats on the floor?
                                                                is it an EVERYDAY driver or mainly a weekend cruiser/show car?       
                                                                has the rust compromised the integrity and strength of the car?
ME/I would clean the spot back to good solid metal... using some sheet metal as thick as (or a little thicker) than the stock
                                                                                      stuff and lap weld the daylights out of it. (maybe climb under the car
                                                                                      if ya feel guilty and smear some RTV or spray bedliner on it and call
                                                                                      it good)                                                                                   
                                                                                   
                                                                                      By the time it rust back through again.you will be too old to drive...
                                                                                       Any future buyer prolly won't notice it or even know what you did.(OR
                                                                                      care) Why put your-self through the torture of butt-welding it..YOMV
6sally6

Dang Sally, that was fun reading. Gave my eyes a workout.

(Glad I could entertain y'all..)
6s6

GPatrick wrote:

It is not much more work to do a proper repair.  It took a lot of work correcting the chicken wire and galvanized sheets that were used to patch my car.  Even if nobody sees it, I'm proud of the repairs I did.

I will credit this to you, but I'm going to use this saying A LOT.

I used the Blair cutters - there are a variety of arbors, pins, and drills.  They are available through a number of tool suppliers and it looks like Eastwood might be selling them.  I used 3/8 and 7/16 for most.  https://shop.blairequipment.com/Blair-Spotweld-Cutter-p/13224.htm

Grinding through the spot welded may produce better results than using a spot weld cutter.  Often the depth of cut is hard to control and you end up cutting into the panel below.  With grinding you can take just a little more off until you just break through. 

I’ve shears, scissors, die grinders bid and small, cutters, polishers and I thought everything in between, but I’ve never heard of a waver wheel. The Internet defines it as something for the lake.