My advise is to steer away from these very small microcontrollers, unless there is a specific reason to use them.
The number of pins has nothing to do with the complexity of the device.
If you want to stay with the AVR's, then the atMEGA328xx is a quite reasonable compromise.
You can stick a single IC in a breadboard and run it if it's internal RC oscillator, or buy small breakout boards such as the "arduino nano". Don't be afraid of either the "arduino" nor the "nano" part. First, the uC is reprogramable by any AVR programmer, so you don't have to fiddle with bootloaders and their peculiarities. The advantage of a normal programmer is that it **just works** (tm) No fiddling with buttons to get it into bootloader mode. No troubles by accidentally erased bootloaders, and other problems with those things.
Also don't be afraid of the "nano" part. It's not so small, it fits in any regular breadboard.
atMEGA328 is factory programmed to run at 1MHz from it's internal RC oscillator. You can just stick it in a breadboard, add two decoupling capacitors and power and it runs. Add a few "dupont" wires for the programmer and you're off having fun with adding more hardware and writing software for it.
And it also runs from less then 2V to about 5V5. You can run it directly from two AA's, 5V tapped from an USB port (or programmer), or a single Li-Ion without even a voltage regulator needed.
A few words of caution:
* Using a powered USB hub between your PC and electronics hobby is always advised. You'd much rather see smoke coming out of an USB hub, then out of your PC.
* Li-Ion cells always need some protection. They just burn too easily. A lot of them have built-in protection circuitry, but taking precautions and putting the thing in a decent battery holder inside a padded metal box (sardine can?) helps containing fire hazads.
The bare chip costs around EUR2 (From an european re-seller, no Ali stuff needed) and you can have either an TQFP (quite small) or SDIP (breadboard friendly) for that money.
If you want to go AVR, then I also recommend to stay with the Mega's. If you don't want to use the "arduino framework" and interact directly with registers, then there are quite some differences between the Tinie's and the Mega's. In my opinion this is a monstrous *&^%$#@! on atmel's side.
With the atMEGA328 you will also not run out of program space quickly, while the tiny chips can get filled with code quite quickly, and then you have to change chips halfway a project.
The atMega328 is as good as any other microcontroller family. It's about on par with the MSP430 I think, and a handful of other brands and uC families. But it's a decent way to start with uC's and it's relatively quick.
The harvard architecture with separated FLASH and RAM is a bit of a nuisance though. Especially when using C or C++ and using text strings. You can work around it (standardized constructs) but a (minor) nuisance anyway.
As a programmer, I've used USBasp for years. "It works" (tm) Atmel used to devise a new programming protocol every 4 years or so which makes switching to other chips also a bit of a nuisance. I once was tempted to bu an "AVR Dragon" Until I read multiple reviews of that thing blowing itself up, depending on what sort of USB cable you use. Yuck.