When you find out what kind of stainless steel you are using, you can do the following to find out if the weld metal you have is going to work.
Find a Schaeffler diagram, (such as the one at this link http://www.ams.ubc.ca/services/exam_database/mmat/mmat377_apr97.PDF if you don't have one handy), and plot the chimistry of the mild steel, and the stainless steel. Also, if you can, do a test weld and section it to determine the dilution you are getting with the welding process you are using. For this example, I will assume the dilution from the stainless steel and the carbon steel are equal, and the dilution of both base metals is 30%. This would mean that the weld is made up of 70% weld filler metal, 15% carbon steel, and 15% stainless steel. After you have plotted the mild steel and stainless steel base metals, draw a line in between them. Since the dilution from each type of base metal is equal, mark a point at the 1/2 way point of the line. (if the base metal dilution ratios change, the point moves towards the base metal contributing the most to the weld in proportion to the percentages). Next plot a point representing the chemistry of the filler metal, and connect a line from the filler metal point to the point you marked half way in between the base metals. Since the weld is 30% base metal, and 70% filler metal, mark a point that is 30% of the way from the filler metal point to the half way point, and that will be the composition of the weld. You want to select a filler metal so that the last point that you found, is above the M + F, or A + M + F region. (above the upper martensite line.)
The reason you want to do this is martensite in your weld will be brittle unless you temper your weld. Usually, you do not want to temper stanless steel as this can lead to sensitization, assuming you are using austenitic stainless steel. If you are not concerned about the corrosion resistance of the stainless steel, this could be an option if you use a weld metal that gives you a partially martensitic weld. The other option, and possibly your simplist, is to try the weld with the 316 filler metal. If your mild steel is thin like your tubes, there will be a slow cooling rate, and minimal restraint on the weld, and you may not have cracking problems. You would also want to consider what kind of service the weld will be in, and whether a possibly brittle weld will matter.
If you find out what kind of stainles steel you are dealing with, and can give more information on the service of the item you are fabricating, please post it or e-mail if you need further info.
G Roberts
The safe method to weld your dissimiliar joint is to use either 309Lsi, 310, or 312 filler material. Gas mix for MIG/MAG 98% argon 2% oxygen will work fine, as will, 98% argon 2 to 3% CO2, welders will prefer the latter. There may be some situations where 308 or 316 filler would be acceptable, like compressive loading only without vibration; the parts service application has not been specified, best to use recommended filler material, above.
With TIG, argon gas is the best. No matter which process you weld the joint with, you must remove any mill scale from the carbon steel surface in the weld zone for good results.
All the above is based off the assumption, the stainless steel is 304/304L or 316/316L.
Hope this helps, Brad