I understand you don't have funds, but personally, I'd pay a shop to weld it up before getting that welder. If you can draw up a blue print and cut all the pieces to size, a welding shop won't charge you that much to put it all together. Probably about as much as that welder and it'll much higher quality. If you don't plan on fabbing up a lot of stuff, I'd go this route.
Otherwise, like the saying goes, you get way you pay for. You might be able to get the thing to hold together using that HF welder, but it'll probably break quickly (welder and piece you welded), you won't have consistent weld patterns, etc. Plus to not even have the option of moving up to gas I think is a bad idea. Personally, if I had to go with a 110V welder as cheap as possible, I'd hunt Craigslist for old 110V Miller (see a Miller 120 for $500 near me). Or go with something like this:
Gives you the option of going MIG later.