To the OP: Glad you are still with us (I read all 11 pages).
Anyway, While I can not tell you what to buy I can tell you with absolute certainty what NOT to buy. Do NOT buy one of those little $90 115 volt flux core wire feeders from the likes of Harbor Freight, Princess Auto, or any other box store offering junk tools, etc. The reason not to buy one has nothing to do with 115 volt input portion either. The reason NOT to buy it is that the real cheapo units are AC output and flux core wire feeding (or even true mig mode with Gas) is a DC only process by design. In other words, There is not a welding wire made by any manufacturer designed to work on an AC output wire feeder. Should be illegal to sell those things but fools keep buying em because they think they are getting a deal. (Note: There are some cheap no name wire feeders out there that do operate 115 volt and output DC. If you dead set on getting an inexpensive wire feeder then look at the output sticker on the unit and verify it outputs DC and purchase one of those instead. Will cost you a few more dollars than $90 but at least you have something somewhat decent and somewhat workable to use that works as intended and you can get welding wire for it. Also there are certainly some high quality wire feeders out there from the big brands that operate on 115 volt input and operate very well within their capabilities).
Unfortunately, There is not one inexpensive do all machine out there. While there are some do everything machines out there they tend to be kinda pricey.
So the question becomes do you want to weld with a wire feeder? (easiest to learn, but gets more pricey if you add a bottle) or go with stick? (cheapest to get into welding with, but harder to learn, and stick does not do well on really thin metal)? Also what input voltage you going to power it with (115 volt or 230 volt?)
As far as wire feeders go: I really do like 115 volt capability for portability, but yes it is much more limiting in what you can accomplish on 115 volt input. I would also like to have 230 volt capability for more power. Back when I bought my Lincoln SP-135P wire feeder (a nice 115 volt unit by the way) a decade or more ago the choices were not as good as today. If I was buying a wire feeder today then I would be looking at the Hobart 210MVP very hard and waiting for it to go on sale. This unit operates on 115 volt at the same power levels as other Hobart 115 volt wire feeders, but also operates on 230 volt just like the bigger Hobarts for when more power is needed. A homeowner is not likely to ever outgrow this machine, but you are looking at $750 to $800 to just buy the welder and that is if you find the perfect sale. Gas bottle lease will further add to the cost.
So here is my run down in order of cost to get into welding:
a) $50 "no name brand" AC output 115 volt input stick welder that looks like a glorified battery charger. These typically output between 50 and 70 amps. Typically these will burn 5/64" 6013 and 1/16" 7014 rods and that is it period. Duty cycle is poor. You can make some limited repairs with a unit like this but do not expect to build much of anything as far as large projects go with it. (I own one of these things, paid $8 for it at a garage sale. I would not recommend one)
b) $100 "used" AC output 230 volt input buzzbox from Craigslist. These are a real bargain for what they will do. Will run 6011, 6013, 7014, and sometimes 7018AC in many rod diameters. Very little to go wrong with one of these simple machines so much so that I would never buy a new one. An old one will last your lifetime, your kids lifetime, and your grandkids lifetime.
c) $200 "used" AC/DC output 230 volt input buzzbox from Craiglist. Adds DC so you can run even more rod choices to your stable. Or even if you continue to use the standard ole common rods that you use on AC then when you goto DC the same rods will run approximately 10% to 15% better on DC.
d) $200 "new" no brand 115 volt volt flux core wire feeder. Expect to be limited to 1/8" and thinner metals.
e) $350 "new" dual voltage stick machine from the import manufacturers like Everlast. Can do stick welding up to about 90 amps on 115volt input or about 140 amps on 230 volt input.
f) $450 gets you into a name brand 115 volt wire feeder that will do flux core (or mig mode but bottle will be extra).
g) $500 gets you into an import 230 volt stick machine
g) $650 gets you into a name brand 230 volt wire feeder(or mig mode but bottle will be extra).
h) $800 gets you into a name brand 115volt/230 volt wire feeder like the Hobart 210MVP (again bottle will be extra).
e) Of course there are much more expensive choices too, but do they make fiscal sense for a homeowner? Only you can decide that.
I know so many choices it gets confusing. If the ultimatee goal is to have the most capability for the absolute cheapest amount of money then that is a decent 115 volt wire feeder (one that can also do mig mode with gas or in other words not a flux core only unit) and a 230 volt used AC buzzbox. Use the little wire feeder on thin metal (where mig mode excels) and use the buzzbox on anything thicker than 1/8" metal but this will take some practice to learn.
If the goal is to have the most capability for the least amount of time invested in perfecting your skills then Hobart 210MVP. (note: A Hobart 190 would be almost as capable but is 230 volt only but would save some coin if dual voltage not desired).