The responses here are all over the place and they all have valid points! One bit of confusion is your scale, I'm taking 1" = 4" to mean that you have some fairly heavy weldments ahead of you. Some of these might be safety critical as such you need to at least consider a professional welder. Correct me if I'm wrong but these would be scale models large enough to ride on, sort of like 7.5" scale railroad sized machinery.
Thank you all for the great information. This looks like one of those instances where if I try to get in cheap I will end up spending more in the long run than if I just did it right from the start.
If what I understand is correct I'd avoid the vast majority of 120 VAC welders as they simply aren't up to the task. There are a few welders that use inverters to allow 120 VAC operation but that usually implies a reduced capacity.
As for welders it took me a long time to get into a position of affording a good welder, in this case a Lincoln SP175. This is in fact a very low end welder but it does do flux core and MIG well. This particular welder is common in fab shops where something very portable is desired, you can actually carry it with one hand.
Now don't be fooled it is still a small welder and does not perform at all like the push around welder (two men by the way) I use to use when I worked in a foundry. You get what you pay for.
My next question would be what is the least I can spend to get a good tig welder? Not including the tank, the safety gear and the helmet. I can't afford a Miller.
You should look into the various welding forums out there. There are Chinese inverter based welders out there that are passable for TIG but there are also many that are crap. You can find people that will comment on specific models. I would urge you to avoid the Chinese route though, in the end it is problematic if you don't have a welding shop already. It is far easier for a professional welder to make use of an imported welder than somebody developing skills. Plus welders have consumables outside of the electrodes, you will want easy access to parts.
Interestingly Lincoln has a new welder out that is multi process and frankly designed for the types of usage you describe. It does MIG, Stick and I believe DC TIG. It is sort of a replacement for the SP175. It is above budget but might be worth a few months of Raman noodles.
I would like to make 1/4 scale car chassis to fit my 1/4 scale ic engines.
Actually I'm thinking a welder might be the cheapest component of this project. Assuming mostly heavy gage sheet metal for the chassis you can get buy with a light weight welder. However you may find yourself wanting to build tools and fixtures to build the care with. An English wheel comes to mind here. I'd feel far more comfortable with a 220 VAC welder than one of the little 120 VAC ones.
If you go to the web site of any welder manufacture you can find the recommended single pass welding capabilities for their welders. That is how thick can the metal be for a decent single pass weld to be performed. In my experience the ratings are a bit optimistic. This is even more so with the imported welders.
By the way one of the reasons I held off so long and went with a US made MIG/flux core solution is the bad vibes I got from people with respect to the wire feeds on the cheap imported welders. Many of them have very bad reputations. This contrasts significantly with the imported inverter based stick and TIG welders.
Now a bit of background, I bought my MIG years ago now and like all things what was accepted back then may have changed. My gut feeling is that most imported MIG or flux core welders are still crap. So even though some of my data points have expired I still have to suggest a US made Wire welder if that is your desire.
Also I learned to weld mostly due to working in a foundry many years ago. They had some very good welders and some really crappy ones. It is truly amazing how much easier it is to weld with a good welder as opposed to a piece of crap. This is why a agree with the suggestions above to get a pro or somebody locally to do the welding for you until you can invest in a decent welder. That doesn't mean extremely expensive but you do need to up the budget by at least 2X to cover both wire welding and TIG.
By the way used is great if you can find a decent bargain. I went to many auctions and so forth and frankly was shocked at the prices some really old equipment went for. Maybe you will get lucky, I eventually gave up!!