Welcome Hi MX372.
The response from gerald_clark is very good, he's technical.
Long post, lots of queries, will do best to reply to stuff i'm familiar with:
-Corebook very good, search old forum posts, don't forget the wiki
-never hurts to keep learning more CLI
-TC calls them extensions, Debian calls them packages
-extensions are like squashed packages containing the binary plus extras, linked into the base filesystem when loaded
-the advantage is once the extension is deleted, upon reboot no cruft left in the system
-extensions are limited, nothing near close to what Debian provides
...but users are encouraged to create and submit their own to the repository
...and developers provide assistance if requested for additional extensions
-TC philosophy is just use what you need, nothing more, so if nobody needs it it's irrelevant
-dCore allows using packages from Debian or Ubuntu but it's still in very active development
-some simple binaries (eg. minimal dependencies) just work in TC but recompiling for TC is best
-lots of other distros run from RAM
-TC has lots of advantages but it depends what you're looking for:
-tiny installation footprint
-extremely customizable
-most extensions compiled to be extra lean
-extremely easy system backup and restore
-community focused and driven
-more RAM is best, but you can operate on old systems (eg 512MB)
-at boot TC will also look for an existing swap partition to utilize (maybe from other Linux install)
-believe TC can also be setup to utilize a swap file, if no swap partition available
-trying to decide on TC is hard, pros and cons
-if you want to learn more Linux, TC is great
-if you have time/energy you'll never get a more customized install
-if you expect 30,000 software packages available, not so much
-if you prefer window managers, great
-in my experience pretty good for old hardware, always workarounds
-depends on what you mean by 'accomplish the tasks you need'
-your hardware specs are decent
-my system doesn't boot from USB either but if you already have another distro installed:
-create another partition for tinycore extensions
-modify Grub/boot loader to point to TC core.gz and vmlinuz
-software
-Firefox and Flash no problem
-wireless drivers available
-youtube no problem
-VLC works great
-not sure about watching purchased DVDs/codec and stuff
-Libreoffice in repository, leaner stuff too
-not sure about wireless printing, can't see why not, CUPS available
-not sure about Arduino IDE
-python stuff in repository
-flburn and brasero in repository
-claws mail and thunderbird in repository
-pictures, choose from eye of gnome, ephoto, flpicsee, viewnior, xfi, xzgv, probably others
-music no problem (choose from OSS, Alsa, pulse), xmms, VLC, others
-see here:
http://tinycorelinux.net/6.x/x86/tcz/-everything working properly, yes but can take some tweaking, especially with hardware limitations
-if something is buggy, report the issue or recompile for yourself
-boot time is hardware and setup dependent:
-TC boots to CLI prompt before reaching coffee cup
-Xorg vs Xvesa takes more time
-adding lots of software to onboot.lst takes more time
-you get to customize however you want, no distribution developer to dictate how it works
-responsive....oh yes...if you set it up right
-if you already like LXLE then why bother, it's probably much more integrated, depends on what you want
-it's good to max memory, that's what it's there for
-i use 32-bit 800MHz single core, 512MB RAM, i'm happy, most users probably would want more
-bottom line comes down to your expectations, willing to put in the time/effort you won't get a cooler system with TC
-if you just want something that boots, immediately works, tons of software available, expect someone else to polish/integrate/work out bugs, maybe stick with LXLE
-i would never tell you to get a new computer