If you're looking to start your own online league I think a much more important question than what do others like is what do you like? When you're, hopefully, going to be putting so much care and attention into an online league it really helps for you to love it in as many ways as possible. For example, say polling everyone tells you that there's a need for a league without financials yet you just don't really care for the slow pace of no financials leagues then it'd really be silly for you to start one because chances are you're going to give it up sooner rather than later. If you haven't already, you really should find out what types of leagues you love and then build that. You might think, well, the market for the league I would like could very well be saturated, but it doesn't matter. If you really love it and put in the effort then it'll rise above the others. You just try to cater to what you think others want and you may very well get it up and running and who knows, someone else might fall in love with it and take it over and it could still be very successful, but IMO if you're going to go through with the effort then you might as well cater to your own likes first and others' second.
That said, take a look at
rem's thread. There's not many replies to it yet and obviously everyone has different tastes or has different ideas of what makes a league successful, but it'll give you some ideas of figuring out what it is you like.
And any time is a good time to start a league IMO. This community has been going strong for about a decade now and it's built up quite a lot of people. The number of people who post here is honestly a drop in the bucket compared to all those who participate in online leagues. So if you build it and care for it well, people will be drawn to it no matter the time of year.