I don't know how the HF lathe is but some of their stuff isn't too bad at all. Years ago I had one of their radial drills and it was dandy, tight all the way around, chuck didn't slip, nothing to complain about. I still have a 7x12 HF metal bandsaw, all cast iron, way better than Jet and a lot lower in price, only thing that didn't hold up was the plastic coolant tank. Depending on the item, more often than not, you can get parts for HF for quite some time especially on machinery when they don't change the design much, if at all, over the years. You may sit on hold with c/s for a while, best to email unless you have time to kill.
As other's said those little lathes are very limited but often come in real handy for doing the little stuff ... I lost a pin in the chip pan on my lathe a couple days ago, the proverbial "needle in a haystack" is a good analogy.
A mini lathe is definitely an asset to have. One thing about it, no matter what size lathe you have, you'll always need/want one bigger/smaller. I have a 14x40 w/ 1-9/16" bore that does almost all I need but I'm in negotiations for an old but lightly used 18x144.
If you're looking for a larger one, 3ph machines can usually be had a lot cheaper than 1ph. There are many different solid state phase converters, I can only speak for the ones I carry, will handle up to 80% of 15Hp and offer the option of variable speed and user-defined time/velocity soft-start on some which give considerable advantage over a motor change and usually at the same, if not less, cost.
Some words of warning when buying an old machine ... just because it's "old" doesn't mean it's worth buying and it's often not worth buying at the price the vast majority of them are priced at. I looked at many over the past year from a 1913 Hendy the seller wanted $1500 for to a 1980's Okuma priced at $9000 - lacking anything short of a total re-build, neither one was worth more than scrap iron less the hauling & handling costs. Occasionally you'll find a gem but more often than not, you're buying someone else's problems like the beautiful looking 14x40 LeBlond I went to look at, seller was firm on the $5k price ... once the tailstock, bed and carriage had been replaced, it may have been worth that price but as it sat with better than 0.100" slop all the way around, it was worthless. What really gets me are those who shell out $1000-$1500 for a 1950/60's zinc gear Atlas with half the gears broken/missing, go on fee-bay and dump another $3-500 for parts then work on it for a month of Sundays only to end up having nothing more than a shined-up #$@*. Think & inspect before you buy!