For SWL general coverage go with something like a Tecsun PL-880. It's lightweight and portable. It has a rechargeable battery and it has real USB/LSB functionality. This will save you some $$$ and allow you to learn about the HF world. It's a love/hate thing so don't be surprised if you get easily frustrated. You can not listen "all over the world" -- so get that fantasy out of your head.
If you have $$$ to spend and want to get something that you can use your TECH license with immediately, then forget the older radios. The 718 is old tech and not worth the money. Avoid used gear for now.
I'd start with a QRP rig. The Xiegu G90 or X6100 is a great investment. They're a little more advanced then the PL-880 so be sure you're ready for that. With a simple TECH license, you can work 10m and if the ionosphere behaves, you can talk quite far with just a simple (easy to make) dipole antenna. You can build one for $20 these days. The G90 is on sale right now and will get you 20w output. The X6100 is only 10w output but has more advanced features and a "easier to read" waterfall display. Again, these are more advanced radios and you may want to get the PL-880 first. FWIW, one big selling point to either Xiegu radio is that they come with built-in antenna tuners.
The Yaesu FT-891 is also a good started rig with 100w output but it has a couple of idiotic bugs. I can't quite recommend it. It also doesn't have an antenna tuner and that adds a $150 to the price.
Great advice overall, but I take issue with the statement that you can not listen 'all over the world' on a Tecsun, and that it is just a fantasy. I have a Grundig G2 (probably performs slightly less than a PL880, but has a similar chip inside) which receives China broadcasting to Europe from Kashgar, and I get them readably sometimes -- just on the whip. I also can hear the transmitters used by religious and other broadcasters in Madagascar, broadcasting to Africa. All off the whip.
I have a 25 ft indoor antenna that is in the room, so it might be adding some signal inductively (through the proximity effect) but I'm not sure of the amount of it. Either way, reception on the G2 is all off the whip. If I had a good, outdoor antenna, of course, I'd probably hear a lot more.
I get similar (and slightly better) results with my Tecsun PL398. So when the ionosphere is cooperating, you can hear the world.
And I live in a hole, in the PNW. So hearing signals on the SWBC broadcast bands from other parts of the world is indeed possible on a portable. Is it a regular occurrence? Probably not. A lot of it depends on propagation. But Tecsuns do rather well off of simple set ups.
Will you get more signal with a proper antenna? Yes.
The QRP rigs you mention sound great, by the way.