These are a couple of my favorites for beginners. If you are looking for a good beginner machine with just the basics then I like Brother Project Runway (this one has lots of fun decorative stitches) or the Singer Heavy Duty (doesn’t have the stitches but it copes well with thicker fabrics). If you want to have simple embroidery capability the Brother SE400 or SE 425 is a good place to start. The Singer Quantum Stylist doesn’t have embroidery but is a good one if you want to do lots of quilting.
Now we are getting into some more complicated territory – you can call me biased here, I do have a strong preference for Janome brand sergers. I tend to use my machines for hours and hours non-stop and find that they hold up better with heavy use than some of the other brands. That said they can be a little tricky to thread the loopers (not that I ever do, I just tie a new thread to the previous color and pull it through). If you prefer a machine that is a little easier to thread then you can try the Brother listed here, though if you want to be sewing rolled hems then just get the Janome, so much easier to set up for rolled hems.
There are a couple of different options here and for me, it comes down to what attachments the machine can use. I am actually tempted to branch out someday and buy more than one brand of coverstitch machine so that I can use different attachments. It helps to know what you want to achieve with a coverstitch before you decide which one to get.
The Brother 2340CV has six attachments you can purchase to add to its capabilities 🙂
The Janome Coverpro has different options.