Once again I'm gonna give you a little reading to do. Hope you don't mind
If you do... well, my advice comes with a money back guarantee so you get back as much as you paid.
Get an external enclosure for that hybrid drive... then you can boot it on any system with a USB port. Er, the enclosures on eBay are very cheap for a reason -- if you go that route, buy five or six, and you should have enough for a year or so.
As for the laptop...
I find the Thinkpad T4* laptops to be very nice, although they have one flaw. I've a T42 with a screen claiming it's a T41 -- there is a design defect in these laptops, where if the laptop underside is pressed upwards (for example if it's sitting on your knee) it will flex the chassis and the motherboard and the graphics chip will come loose. So I had a T41 with a nice screen and destroyed graphics, and a T42 with a low-res screen and working graphics. Swapping screens gave the best of both in one. These laptops are common on eBay for about $100-150 depending on how much work you want to give them. (The upper price range is for "comes with battery, charger, and --sometimes-- HDD".) I'll note that IBM's computer division became Lenovo in 2005, and I don't have anything new enough really to speak to the brand after that transition.
Dell is a good brand as long as you don't have to pay for repairs, and they have nice support as long as you're under warranty (anything from eBay is not!). Extended warranties are expensive but (in the one case of Dell laptops) possibly worth it if you purchase an exceptionally troublesome machine. The problem with Dell is that, like the other major brands, they do not conform to physical design standards. In the case of laptops, this isn't an issue -- there are no such standards other than for drives and (sort of) LCD sizes. Dell desktops, on the other hand, tend to make my eyebrows go up when I look inside.
HPs new and old are okay -- but their tech support is universally described as horrible (or worse). If it breaks, you're on your own.
ASUS makes nice computers. If you like tiny screens (11" or smaller) get an ASUS netbook. Just don't blame me if you get eyestrain using it! Full disclosure: one of these with a 10.4" screen was my main system for three years. I now have a handmedown Dell Inspiron 6400 with a 15.6" screen and it is so much nicer on my eyes. I wear glasses, to boot.
Last but not least... my mother has a Sony VAIO VGN-S360. It chews through hard drives rapidly (I think it's a thermal issue -- a CF card + IDE adapter would work well here!) but other than that it is incredibly durable. It has a nice screen, 13.3" IIRC -- but with insanely high resolution possibilities. The only other issue with it is that it takes a very strange style of RAM called MicroDIMM that is rather rare both in stores and in systems (eBay is good for this sort of thing).
Mind you all of these are not terribly powerful machines. My ASUS netbook has an Atom processor. The Thinkpad and VAIO both have Pentium M CPUs, which are about ten years out of date. My Inspiron is a little newer -- it originally had a Core Duo in it, but it now has a Core2Duo and it is great stuff.
If I were going to put a Puppy on each of these machines, here's what I'd use...
ASUS 1000HEB Netbook: Fluppy or (older) Puppeee, mostly for the extra drivers. Puppeee is actually the first version of Puppy I ever used, although I don't remember what version as it was some 2.5-3 years ago.
IBM Thinkpad T42: I use Puplite 5 on this a lot (Akita Linux is a newer version of same) and it's pretty speedy. It could probably handle Wary just fine, but anything with a PAE kernel (eg Racy 53) will not boot. Not sure about Slacko 533 -- I'll have to check.
Sony VAIO VGN-S360: runs Puplite 5 pretty well. I'd actually recommend Akita here, something more powerful will need swap space as this particular example only has 1gb RAM in it and it's technically maxed out*.
Dell Inspiron 6400: any Puppy you want. I've run jejy69's GNOME-Slacko a couple times on this thing and it is FINE. Heck, it'd probably handle Lighthouse64 just fine if I wanted it to... I had a bad experience with that particular Puplet once, though, so I know it's not for me.
*You can get 1gb MicroDIMMs on eBay for a ridiculous price and up the RAM to 2gb without much issue... but I haven't done that, mostly because of the expense. That stuff is NOT cheap!