Single travelling in Sep-Oct - which destination: China, Russia, Barcelona + Portugal, or Cuba?

September/October is certainly not the best time to visit Cuba, because of the cyclones.

The other three look fine, and can be done alone. Which one to choose is mainly a matter of budget. All else equal, the "Barcelona + Portugal" will be the least costly option.

If I had three weeks and the necessary budget, I would pick Russia and China from your list. More precisely, I would travel on the Trans-Siberian Railway from Moscow to Bejing. Note that this site has some resources on that topic.

I had the best travel experiences, while traveling alone. I can at least confirm that China can be traveled alone. Traveling alone is also the way to meet people. Buy yourself à lonely planet and you'll see that you'll have an instant new social network. You'll keep meeting people you already met in previous visited hostels/hotels/places

I have travelled alone to Cuba, Spain and China and I didn't have any problems in any of those countries. Like the previous answers have stated, Cuba would not be a wise choice for that time of year. Otherwise, that would have been my first choice. Spain and Portugal are easy places to travel in. China, on the other hand was a little more challenging to get around and get myself where I wanted to be purely because of the language barrier.

I would highly recommend, as a solo traveller, to stay in backpackers, no matter where you are. There are loads of other people doing the same thing as you and you get to meet awesome people who can really give you some great tips. And gives you the possibility of doing day trips with other foreigners for those days you want to socialize.