Graham-xrf,
Yes, when I said Flux-core, I was referring to a machine which looks like a MIG welder, except it does not use bottled gas. The welding "wire" it uses is actually a "tube", which has flux in the core. As it heats up, not only is flux released, but the high heat converts the flux in the center and produces gasses which help shield the weld puddle as well (not to the level of a real MIG welder). However, what has not been mentioned is the fact that flux core wire welders are much more friendly to use outside (a building) than classical MIG/TIG welders. When Using a classical MIG/TIG welder, your "shielding gas" (CO2, CO2/Argon, Argon, Helium) can get blown away by an outside breeze. It is the pocket of protective shield gasses which prevents the weld from getting ugly. When that pocket of gas gets blown away, it produces a result inferior to flux-core wire welding. This means welding "location of use" matters. If you intend to ALWAYS weld inside, then Gas-Using welders (MIG/TIG) are excellent. Flux-core welders are inside/outside welders. There is no question that gas using welder produce a "prettier weld", However, until you develop some skill, don't always trust pretty. Do some practice welds and then cut into them afterwards to inspect the quality of the weld. In the USA, a lot of farmers prefer Stick welding with flux-coated rods, as much of what they weld (farm equipment), has thick metal, AND they frequently must do their repairs outside.
I got started with stick welding, as it was a very economical way to get started. Many years later I got a flux-core wire welder (which to the casual observer looks like a MIG machine, but without the gas cylinder). For thin stuff (5/16th inch 8mm) or thinner, it works rather well. There is no question using a gas welder would produce prettier welds which would not require a wire brush to clean off the surface slag. Flux-Core welders are (for the most part) welding steel. Gas welders open the door to weld other materials, such as aluminum, or with TIG, even titanium. I have seen skilled TIG welders do amazing things, such as weld two thin-walled beer cans side to side with each other (that was the employment proficiency test in a shop I worked in for people who claimed to be TIG welders). This task was made more difficult, as they were not allowed to do surface prep. A blow-through, or a bad weld was a fail.
My main caution is that so many people buy welding equipment which does not match their eventual needs. Getting started with something cheap gives you time to get a feel for what your needs actually are. It gives you a chance to figure out your scale of use. It gives you time to sort out other details as well (location, grinder/wire brushes, Helmet, gloves, apron, welding table, clamps, etc). If you learn to weld correctly on a low-end machine, your welds on a high end machine will just be better. In the past I have been guilty of buying the tip-top super version of a tool, only to discover I only needed a fraction of the capability. This experience has made me cautious, and now I tend to dip my toe in something new, before taking the full plunge. Oh, and the cheap welders can frequently be sold for about 3/4 of their purchase price, as it seems that the market for inexpensive welders is always an active one.
Some day I may get one of the high end, water cooled TIG rigs, which is multi-process, and can do MIG and Plasma cutting... but for now, those are not critical needs for me. Figure out your real needs, before opening your wallet. I realize this advice is the opposite you frequently get in this group, which will frequently suggests you buy the maximum. If you do decide to get a super-machine, then some welding classes would be merited, so you gain the full value of the equipment you purchased.
Best of luck with your choices, I know they are not easy.
Addertooth.