My advice is to go to a proper bricks and mortar shop if you can, and one that specialises in sewing machines rather than a department store like John Lewis because the staff will be much mor knowledgeable. They might also have a good buy on a second hand machine which has been traded in for a fancier mode and/or prepared to allow you to trade-in at a future date if you want to upgrade.
Take a few pieces of fabric with you to try the various machines with; cut off jeans leg, the back of an old lightweight cotton shirt and the back of an old tee shirt will suffice.
If you have to buy online
Sewing Machines Direct are very good. Make sure you avoid the company which, under various incarnations, promises unrealistic 25 year guarantees and has been featured on
Rogue Traders. Do your homework, and set a budget.
Ask yourself; do you need a machine with lots of fancy stitches, or just a few basic utility ones such as zig-zag, triple zig-zag, overcast, blind hem etc?
Do you need a machine with oomph in the motor so as to be able to sew heavy fabrics such as denim. The hem on a pair of jeans means sewing through nine layers of denim; a lot of low end cheapie machines won't do that even with coaxing the fly wheel.
Vintage machines can be a very good buy, but the old black Singers only do straight stitch. They do that superbly well but it is restricting not to have the now standard utility stitches. The buttonholer attachment for vintage machines will make a buttonhole as good, and often better, than the automatic buttonholes on high end machines.
Will you be wanting to sew jersey and other stretch fabrics - tee shirts, fleece hoodies etc? If the answer is yes then seriously think about an overlocker as well. An overlocker is also very useful for finishing the raw edges of conventional machines.