You could use something like Kickstart, which is a feature of the anaconda installer of Fedora, CentOS, RHEL, and derived distributions that lets you completely customize an installation to your liking. You can choose which packages you want to install, the partition layout, network configuration, package repositories, root password, and much more. You can also create pre and post-installation scripts that do whatever else you might want. You can run the install fully automated, or pick and choose what you'd like it to prompt for. All settings are defined in one simple (not XML) text file, which you can make by hand or with the graphical system-config-kickstart tool.
Once you've got that put together, you can roll your own custom CD if you like, or set a network location in your kickstart file, which can be a local or Internet mirror, via FTP, HTTP, or NFS. Your kickstart file can also be on the network, so you can just burn one stub install disc to bootstrap the installation (or use vanilla install media) and have it use as many different configurations as you can stand. You can even network boot it, eliminating removable media altogether.
The network options or custom spun media eliminate you from needing the "huge package repository", yet it will still be there if you decide you want to add something. But, if you want to go whole hog, you can build your own repository, cherry-picking RPMS from upstream, customizing SRPMS to your liking, rolling your own, or even hacking a make && make install or tar -jxf into the post-install script.
Many distributions have similar functionality, some of which also understand Kickstart files even if they don't implement their entire feature set (like Debian).
What you are looking for is pclinuxos, it has a live usb installer on the live cd menu. Once installed to usb and booted it offers a menu for either live boot or live with persistence.
My install of the 2009 was what you desire... I am just testing the 2011 offering but it has a difference in that it boots live by default rather than persistence which is even better for you.
Best Answer
Slackware should do.
And to be honest - there is no "standard" linux.
You define your standard afer you defined what you need to do with it and what to expect from it.
The low-level (plug and play, device-naming, network configuration, system configuration, detection of network services, hardening) is quite different on different linux distributions. Even init-scripts and how they get processed during boot is different.