First off... I am a self confessed sewing machine snob. Therefore I don't want to address brands here. That opens us up to the same what brand of hammock/tarp/sleeping bag etc should I buy. We all have our favorites and we all have those we wouldn't touch if it was the last option on earth.
I am more concerned with the questions How do I buy a used sewing machine? What do I look for?
For the first time buyer my best counsel is, was and always will be the local sewing center. Chat up the mechanic and share his enthusiasm. But the craigslist/ebay market is very appealing. It can however be scattered with pitfalls a first time buyer needs to be aware of.
1) Don't buy in haste. Unless you know what to look for, going to see a used machine (often an option on craigslist, not so much on ebay) is not likely to be helpful. If you know what to look for then you don't need this thread to help make the decisions. Find someone who can go with you if that's what you are going to do. But feeling under time pressure to purchase usually leads to bad choices. So take your time. Take some lessons first. You usually don't need to own a sewing machine to take sewing lessons.
If you are going to buy on the public used market here are some questions that I think you might want to ask.
2) Are you the original owner? The farther removed from the original owner you get the murkier the information becomes. "Well, it was my mother's machine. She died and we are selling off her estate." So you can't talk to the original owner.
A: Get the exact make and model number of the machine. If the seller can not provide that minimal information then pass on it without question. When you have that, make a few phone calls. Call, the local sewing center and ask if that machine is still serviceable. Thread injectors are machines and all machine need maintenance. If it doesn't need it now it will some time in the future. Parts for older machines, particularly brands no longer being produced can be very hard to get. Consult the experts before sinking money into what will become an over-sized paper weight.
B) Yes.. I am the original owner. You may have struck pay dirt here. Ideally this is the person you want to talk to.
a) When was it last used? The longer it has sat unused the more likely it is to need servicing. Sewing machines are complicated pieces of machinery. The drier the machine is the harder the lint and dust and crud inside gets. The harder it gets that more skill is needed to remove it without damaging the machine. Remember a sewing machine works on the idea of close tolerances. Sloppy gears and wobbly bearings or bushings can make a machine not work properly but also wear it out sometimes beyond repair. The more recently it has been used the more likely it is be in decent working order.
b) Why are you selling it? This is a very important question. Well I bought a new machine and this has been sitting in the basement/attic ever since so I thought I'd sell it. (See above) FYI the basement and the attic are two of the worst places to store mechanical things. The damp in the basement and the heat in the attic are death to bearings/bushings and other moving parts. I used this machine for years but I can't make the dresses I want for give my granddaughter with this machine, so I just bought a brand new machine with all the fancy stitches. I don't need this one anymore. You hit the motherlode. This machine is most likely gold for the gear maker. If you think the price is reasonable (research the market) buy it with a fairly high level of confidence. Unfortunately these machines are also somewhat rare.
c) Why did you stop using it and when? This is combination of the two questions above but also a question in its own right. If it was because of frustration on the part of the user... you can expect to be frustrated too. Assume with an older machine being sold by an older owner the frustration was not user error. That may be true, but more likely the machine needed service then and will need more service now. "I had a stoke three years ago and I am moving to assisted living. I won't be needing it anymore." That's worth a serious look.
d) When was it serviced last? "Oh we had it serviced when we decided to sell it!" Ask to see the service record. If they had it serviced for the purpose of selling it they would keep that. You want to see it. If they can't produce it don't expect that to be the truth. "It was serviced about 4-5 years ago while mom was still using it." It is likely worth a serious look if the other considerations meet approval.
3) I know nothing about sewing machines but I got favorable answers to the basic questions. What should I look for when I see the machine?
A)"OOOO Shiny!!!" The shiny parts should be bright and shiny. Smooth, polished and shiny. If you see pits and corrosion on the places YOU can get to then the places you _can't_ get to are going to be even worse. Remember they probably cleaned it up before they put it up for sale. But just cleaning won't hide the grit, pits, dimples and corrosion that will interfere with the way machine runs.
B) Put some fabric in the machine. Take it for a test drive and _listen, listen, listen_ Listen to the motor at all speeds. You should be able to run the machine slowly enough that you can see the needle eye go up and down. Every thing should smooth and easy going. Make note of any laboring that hear or any ticks, tocks, stutters or pauses that occur at low speed. Floor it!! The machine should be stable and balanced on the table. It shouldn't jump, bounce or make you chase it around the table. That would indicate a machine that is out of balance or alignment. Not a good thing. If it is just a timing thing, that is likely worth fixing. If it is out of balance you have major problems. Pass on it or buy it for decoration but don't expect to make good projects with it. Clicks and clacks, motor lugging, Bouncing around all indicate that service is warranted unless you are buying a disposable toy.
4) Study the test stitches. Learn what good stitches look like. Learn how to make the stitches look like they should. If you like what you find out, see and hear then make an offer. If you think service is going to be needed figure that into the price you want to pay.
There are very few of these guidelines that would nix a sale if and of itself for me. But they are guidelines to help your expectations be realistic. Nothing is worth than spending more than you want to spend for a machine that needs servicing before you can use it.
The above post is not all inclusive. I am sure others can add things that I didn't think of or just didn't add.