Nothing wrong with a bit of "overkill" it's often why an older vehicle can be relatively cheaply brought back to life and is strongly to be recommended with the old horticultural machines I mess about with.
Cebora - pronounced Chebora I'm told? My MIG is a Cebora Pocket Turbo 130. It's the same machine rebadged as Snap On and was sold out of their vans (for more money) and an excellent machine it is too, had mine for a long time and the only problem I've had is with the switch in the handle itself which controls the wire feed, It's not a very robust design and needs to be dismantled about every 2 years and have it's contact faces cleaned with some fine grade emery, then it's good to go again 'till the next time. The rest of the machine has never even "blinked"! Can't remember when I bought it but I've had it for a long time.
The other excellent welder I have is the first one I ever bought. It's an SIP Topweld 140 stick welder. bought in the early 70's. I've made and repaired shed loads of stuff with it. Welding up cultivator chassis, making my own small (5ft x 3ft) unbraked trailer and many other projects. The only problem I've come across with it is that because it's a machine at the cheaper end of the price range (I was an impoverished and ignorant youngster when I bought it) it's transformer windings are aluminium. If I was buying again I'd go for one with copper wires. In fact the aluminium core works very well but has a basic flaw. I found this out one day when welding with it and found it getting increasingly difficult to strike the arc. This got worse until one day I gave up using it, thinking it was knackered, and parked it under my workbench where it stayed for quite a number of years. Luckily I had access to welding gear at work so just used that. Then when I started doing the evening welding classes I found that many of my students were wanting to learn on machines like it - I encouraged people to bring their own machine in with them and learn on their own machine because these cheaper machines can be quite different to use, especially regarding striking the arc which depends on having a good open circuit voltage and can be quite marginal on really cheap machines. So, as some students hadn't yet bought their machines, I hauled the SIP out from under the bench and set about finding what was wrong with it. It turned out to be very simple. A friend at work who was a professional welder (north sea pipes) helped me dismantle it and we found the connection between the aluminium windings - which were formed into "eyes" by bending the wire round - and the steel output terminals was poor due to a build up of corrosion ( I now know this was an electrolytic reaction between the aluminium and steel of the terminal. I gave them a light clean up and made sure the connections were tight and it worked probably better than it ever had even when new! I now find that a very light clean up every couple of years and a light coat of ceramic anti seize completely cures this problem. I've since resurrected a few of these welders with this same problem and I'm always keeping my eyes open at autojumbles for cheap machines because often that's all they need to completely restore them to full usability again.
Don't know how many of you are into doing stick welding? but in case it's useful some of the more common problems my beginners had were:
Using the "wrong" rods. You need to be using a good quality general purpose, all position, RUTILE rod. Buy from a welding supplier who will be able to advise you on what's best and probably be cheaper too.
Don't expect too much from the machine. These small machines are all air cooled and many don't even have a fan. Mine didn't and would overheat and cut out when welding heavier gauge stuff. All but the cheapest will have a thermal overload which cuts it out if the windings get too hot. Then you have to wait for it to cool down before it'll work again - could be half an hour - but if you just start welding again right away, within a very short time it'll get to hot and cut out again because it wasn't fully cold when you restarted. By the way, these cut outs can fail so if your machine was working fine and suddenly cuts out and then, after waiting for it to cool, it still won't work all it may need is a new cut out which is cheap and easy to change.
Don't expect it to give you a long weld time with thicker rods. My machine - SIP topweld 140 - claims to be able to handle 3.5mm rods, and it will, just, for a very short time. I find it much better to accept that it works well with 2.5 (and smaller if you get good at it - small rods are much more difficult to work with). I've also installed a cooling fan into the back of it's cover and blanked off the rear louvres so that air is pulled in over the transformer core from the front and expelled through the fan at the back. It now very rarely, if ever, cuts out when using 2.5 rods. As a little guidance 2.5 rods are ideal for welding stuff like angle iron and plate. You're not going to weld car bodywork with it. Even with a 1.6 rod you've got to be very good to weld stuff like wings and sills. better to buy a MIG if that's what you want to do. Unless you're only going to use it very occasionally, it's worth splashing a little more cash for one with a cooling fan and probably, as it's going to be a bit more "uprange" it'll have copper windings too.
Electrical supply. Don't expect to be able to take the welder down to the bottom of the garden, plug it into your power tool extension lead, and expect it to work. It'll "fool" you into thinking it's working because when you switch it on it's lights will light up and the core will probably "humm" but it won't be able to pull the current it needs to weld and, although you might get a spark, you'll find you can't strike the arc. I have a 15 meter 2.5 wire size, 3 core extension which, when plugged into the welder's own supply cable allows me to work anywhere I need in my workshop and that's probably about as far as I think I could stretch it. I would not use this extension unless needed though and plug the machine in on it's own cable wherever possible. So you need nice thick cable size and not too long otherwise the current drop in the wire itself will stop it working. The shorter the better is the way to go.
I'm sure there's much more I could talk about but the above is agood starting point. I find welding very satisfying to do and it's amazing what you can do once you've mastered the basics. You do need to learn some technique though and a short course will rapidly bring you up to speed whereas trying to just muddle along on your own will take much longer. Don't think these wee machines are "toys". you can easily hurt yourself and others if you're not careful but also you can make and mend some really ambitious stuff. My biggest achievement was to build my own trailer. 95% of it being welded up with the SIP stick welder with only a few little brackets added later with the MIG. I'm very proud of it so here's a picture for you all to go "awe" over. It's loaded up with my gardening gear ready to go off for a day's happy gardening at my boy's house :
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. Thinking back, did yours have a sort of clutch arrangement in the back of the electric motor to help it kick in, the motor does look familiar. The one I replaced it with is an old V twin Bristol compressor, the only thing that gave problem was a big end bearing I recall and you undid a small plate to access it and it was a cheap standard type bearing. When you see all the modern Azenda Spanish type with aluminium barrels etc. scrapped because they aren't worth fixing, I suppose that is the reason by British industry went down the toilet, people only needed to buy once! I bought the Bristol one from the widow of a mechanic who ran a little workshop near us and used to do king pin reaming and other bits for people. Another thing I recall I didn't buy, but was there in tissue paper was a set of brand new Nash Metropolitan hub Caps, how many times are you going to see that? 
