I don't know if it helps, but I'd offer the following;
If you can, get an inverter welder, whatever sort you get. Modern inverters are so far ahead of any of the old fashioned transformer machines its just not worth thinking about buying a new transformer welder now. It will make your newbie welding experience better in two different ways.
Firstly it will make your welder easier on your power supply. Transformer welders have all sorts of extreme electrical demands, which inverters eliminate. With a marginal supply an inverter will do a better job of giving you a stable arc.
Secondly, if you give an inverter a less good supply than a transformer welder, then the inverter will still give you a more stable arc.
Internally, inverters make use of closed loop control and this affords better consistency of electrical output. In electrical terms, a closed loop regulated supply has better load *and* line regulation than an open loop scheme like a raw transformer.
When you then add to this that inverters can be dynamically controlled, you begin to see incredible capabilities like "arc force" control emerge. I know you are not explicitly looking for "ghastly stick welder" but if you get any kind of inverter welder, you probably want to be looking at a "multiprocess" welder, just to get value for money. Normally this would be MMA (stick) and some other capability. So if you get a multiprocess welder make sure it has an arc force control. If it has "arc force" then it is no longer a "ghastly stick welder". The two are mutually exclusive.
There are very few situations where your old transformer welder will outperform a new inverter. If you get a DC only inverter then, when doing MMA you can experience "arc blow" when say approaching the inside corners of angle iron. An AC transformer welder will help in this scenario, but it's the only one I know of. If you are worried about that, then get an AC/DC inverter.
Generally you are going to find two kinds of inverter welder, MIG/MMA, TIG/MMA. You can get MIG/TIG/MMA machines, but normally they're in the "Tom Lipton" realm.
Naturally, MIG welders will focus on the benefits of having a wire feeder, and if they are multiprocess will switch between constant voltage (MIG) and constant current (MMA). In a general sense, any welder that can do MMA can also be converted for TIG welding, and given that a MIG welder will have a gas valve, it will probably do TIG welding better than most. Why would you then bother to get a TIG/MMA welder?
TIG/MMA welders do not usually bother to provide a constant voltage capability. Obviously you can get separate wire feeders, but these are the "Tom Lipton" territory. If your machine cannot support constant voltage then a wire feeder is not going to be useful to you. On the other hand, proper TIG welders will usually offer an AC capability.
An AC arc will help in certain MMA situations as already described. Critically AC is pretty much a requirement for Aluminium welding. If you get an AC capable TIG welder make sure it has variable AC balance. This allows you to control the cleaning action. I won't bother with that here but if you end up welding any aluminium you're going to be very interested in that.
Most TIG welders come with a variety of pulse options, slopes and ramps, which can work with your foot pedal. These features are easy for manufacturers to offer, but I must admit to not using them much. For TIG the foot pedal its self is not mandatory, but do get one because you will want to use it.
If you go for TIG, reckon on getting more than one torch. A high current torch will be clumsy on delicate work. A delicate torch will quickly overheat doing high current work. I won't talk about water cooled torches, I understand that these are the panacea, but they are a bit "Tom Lipton" for me.
If you get a Chinese welder it might be quite good. Mine is German badged, but made in China. It's all right, and I would recommend one. Be mindful that Chinese welders generally have metric gas fittings. Most US/English welding equipment is….. English. If you have a lathe and a bit of imagination this isn't going to bother you too much.
I really would recommend TIG, for the workshop. TIG is definitely indoor welding. For jigs and fixtures it is perfect. You can do the smallest of welds with ease. For high temperature fixtures it is a godsend. For any "visible welding" TIG is "the way".
If you do a lot of sheet metalwork, perhaps MIG is the way. For sheet metalwork TIG cannot do everything that MIG will do, but if you're not happy with a lumpy seam on the inside of your outer wings on the car, TIG is still what you're going to need.
TIG is technical, but if you're happy with that, you'll do fine. Quality MMA welds are *MUCH* harder.
For TIG you need a bit of brain. For MMA it's less brainy, but you really have to have actual skills if you want anything approaching a proper weld.
MIG can give you a proper weld on heavy plate work jobs, but on light work it will never be "nice".