So I want to try making my own patches

If you mean small pieces of already patterned fabric to sew onto larger textile products (clothing, bags, etc), that you can just cut and sew by hand.

If you mean stitching complex patterns or symbols with multiple colors of thread, that’s something you do with an embroidery machine. These are mechanically complex - they are more work to set up, more fragile, and more expensive than a standard sewing machine. They are also not very good for basic productivity stitches (e.g. seams) as they are intended to make very fine stitches on relatively lightweight fabric. They are not good starter machines.

For general sewing work, and especially for learning, I recommend any machine that does not have a screen like this one:

https://www.brother-usa.com/products/ps700

These types of machines are common at entry-level prices, and they offer a wider variety of stitch options, but realistically you won’t get much use out of those, and in my experience the embedded computer parts make the machine less reliable.

I prefer something purely mechanical like this:

https://www.brother-usa.com/products/st531hd

All the controls are physical knobs, dials and switches - no touchscreens or touchpads, no computer components, no vague error messages. It’s mechanically simple to the point where there is very little that can go wrong with it - it just does the job.

This model is also heavy duty, which means it has a stronger metal frame, a stronger motor, and more metal parts in the construction in general (over a standard duty machine). It should last basically forever. Other machines may be able to take heavy duty needles, but that doesn’t mean the machine itself can actually punch through 4 layers of denim without stalling or twisting the frame. Even if you don’t end up working on a lot of heavyweight fabrics, a heavy duty machine will suffer less wear and tear from normal use.

Why would you need to punch through 4 layers of denim? Because when you make a seam in a pair of pants like this:

you overlap the two pieces of fabric and then fold it over and stitch through it like this:

https://en.wikipedia.org/wiki/Felled_seam

In the places where multiple seams come together (like where the pocket meets the side seam) there will be even more layers, and an otherwise easy project can suddenly become very difficult to complete when your machine just can’t handle 8 layers in a double-over seam.

Um… one possible downside of a heavy duty machine is that it will sew through your finger if you’re not paying attention, where a lighter duty machine might jab you and then get stuck. It’s also heavier to pick up and move around. It may also have less throat space:

than a similarly priced standard duty machine, because the longer the frame pieces are the more flexible they are. More throat space makes every kind of project easier because there’s more room to feed the fabric through, but it also makes the body of the machine more fragile. If you think you might work on larger projects (like blankets/quilts) you may want to prioritize larger throat space as a feature (dedicated quilting machines have longer arms to accommodate larger pieces of fabric).

Don’t be afraid to buy a used machine, but try to find a copy of the user manual for it before you buy it. Especially starting out, you’ll want the instructions for how to set up your particular machine, and how to do basic maintenance and troubleshooting. All mechanical devices require occasional maintenance. Looking at the manual should also help you figure out if the used machine has all of its parts.

Whatever you buy, keep in mind: simple is good, simple is reliable, simple is difficult to break accidentally and easier to fix if necessary. Extra fancy features do not make a better machine.

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*Edit: also don’t buy one of these cheap portable/handheld type machines:

https://sewingmachineguide.co.uk/guides/best-handheld-sewing-machine/

Don’t waste your money. The little handheld ones can have a use to get into weird angles or small spaces that would be impractical with a normal machine, but only in very specific situations. They aren’t general purpose machines.