Well my 2 cents is this:
First, I highly doubt that your Lincoln tombstone is dead. I imagine it just needs some work done on that selector switch which is really pretty easy to service. There are many rebuild threads around on servicing that switch with photos included (e.g. welding web). All parts are still available probably $10 worth of parts at most and you be good to go - and you may simply require a good cleaning and not need any parts. If you are as cheap as you claim then absoluletly nothing will last as long as an old AC welder - your grandkids will still be using it. If you shop craigslist then you might even luck out and find one of those old add-on DC rectifiers for like $30 to add DC cabability to the unit you already have.
AC/DC tombstone (or Miller Thunderbolt AC/DC or Hobart Stickmate AC/DC). I started out with a Lincoln AC225 and several years later found an older Miller Thunderbolt AC/DC at a good price. Comparing AC stick welding on each I think the Lincoln was slightly better on AC even though it was tapped setting and Miller is infinitely adjustable. I kept the Miller because it was DC though. DC allows you to run some exoctic rods (I never do), some arc starts are smidge easier (not earth shattering easier), some out of positions are supposedly a tad easier (I suck at any OOP anyway so...), if you lack mig then I do think DC biggest advantage is stableness at really low amps and the ability to switch polarity again at really low amps to avoid burn through on really thin metals (you have mig already so doubt this is huge benefit for yah). For me, I burn the exact same rods that I did when I only had AC now that I have DC and notice little difference on anything above say 60 amps. Lastly, you can add a scratch start tig torch to any DC output welder and do scratch start tig. I have done this simply because it was cheap $45 for the torch, already had an unused bottle and regulator. I have yet to really need it, but has been fun to play with. If you want to add tig torch then definitely go Miller/Hobart over the Lincoln for the infinitely adjustable amp setting over tapped. AC/DC transformer almost as durable as AC only units but Diodes will eventually fail, but easily replaced by homeowner without special tools so likely to still provide decades worth of trouble free service.
New Inverters: I have never welded with one. Lighweight would be nice if you need portability (I do not), Dual voltage operation would be nice (I do not need that either though). I imagine the arc force would be nice (Have not needed up to now though). You are not going to weld aluminum with low dollar inverters as they are DC only so no different than DC on a transformer in that regard. Inverter will use 15-20% less electricity than comparable transformer machine. If you are welding 8 hours a day 5 days a week then this electricity savings can add up. I weld only when needed so electricity savings is mute point for me. Plus I use "Twin Carbon Arc torch" for free source of intense heat for bending metal, freeing rusted nuts, brazing, etc. and you can not run "Twin carbon arc off an inverter" without frying it so that totally rules them out for me. For me, I do have no doubt that inverters can be nice and they have their place for some people, but their are lots of circuit boards that are eventually gonna fail (when who knows) but more than likely in 5-10 years you are going to need either service on it or replace it again totally because that board is no longer available. Pretty much like this computer that I am currently typing on. It works great when it works, but I have never gotten more than 6 years out of any computer before it died with failed components rendering it cheaper to replace than repair. My computer is stored in my climate controlled house. My welder is stored in my old barn that is unheated, leaks in spots, has a dirt floor, and sweats sometimes when there are drastic temperature changes. Not an environment that bodes well for electronics but will not hurt an old AC tombstone or AC/DC buzzbox one bit.
Now if I made my money or living with a welder, then I might change my mind. Having the best of the best might matter on something you are selling. Replacing high dollar equipment is not a problem if you have enough revenue to justify it - you simply pass those costs along. For me though, I am just a guy like you that repairs ole junk farm equipment and totally prefer durability and low cost over all other things. I have no one other than myself to pass high costs onto, and I simply do not use a welder enough to justify expensive equipment that is also highly likely to eventually break.
Ooh boy- sorry for the long post - LOL
