Having gone down this path, I can tell you that you will likely be disappointed with any form of low power diode laser, like both of those that you linked. Yes, they work, but slowly, and with limited materials and thicknesses. They are great in the sense that they’re typically very cheap, require little or no support equipment, and minimal maintenance, so for a beginner, they are a logical starting point. But that’s where it ends. At 10 watts you can engrave, but cutting will be limited to very thin materials. Yes, you can do multiple passes and this does work, but only to a point, and each pass tends to cause more and more burning of the edges. Also, without air assist, the debris from each pass tends to collect in the groove so subsequent passes just reburn the stuff you’ve already cut rather than making additional progress.
If you can swing a little more money and are willing to deal with some extra setup and maintenance, I would go with a k40 style CO2 machine. MUCH more power means more speed, deeper cuts, and a CO2 laser will add several materials to your capabilities list that a diode can’t touch (clear acrylic for instance).
FULL DISCLOSURE: I am a demo room and affiliate for Omtech so I do get a cut of any sales through my affiliate links. That said, I am an Omtech owner and have run several of their larger CO2 machines and a MOPA fiber laser so I practice what I preach when it comes to their stuff. IF you would like to go down the CO2 route, I am happy to help and can get you a small discount on whatever you buy (IIrc, it’s only about 5%). If not, no worries, I hate being a salesman and won’t bug you about it, I just don’t like seeing people who are just starting out make the same mistakes I did. I went through 3-4 different diode lasers back when CO2’s were crazy expensive and while it did help to build my knowledge base, given the availability of machines these days, I definitely wouldn’t do it again.