Singles first. Then the album. 3 to 4 singles is not uncommon
Things change with the seasons as does general mood, so there is some validity in generalising to time the mood of a release with that season. In truth some songs can be successful at almost any point of the year, songs targeting seasonal markets obviously depend on the season, and some songs mood is not associated with a specific time of the year.
The mood people are in can make a difference to the music they select to play and to buy. Spring people tend to be more up, excited, anticipating a good summer, but any season can be subdivided further. I have no doubt some psychologists somewhere will have it all charted out and that marketers are aware of such studies and use them when determining product launch dates.
2 to 4, though for a signed artist it depends on the deal, and for all, the later singles existing at all can depend on the revenue from the first launches.
Exact time scale, and even song choice, are determined by how the market reacts. 2nd singles are usually released a month or two after the previous single has passed it's maximum number of units per day and sales have begun to decline. Singles are used to "warm up the market" as much as make sales. At all times marketers seek to release at the optimum point, when they can reach the largest number of people with the optimum product in the optimum way.
Whenever we get over a hurdle of parting with money to buy something, in the moment you do that you are at your most likely to make another purchase. Yes other things can affect that, but it is the ackowledged best time to make another pitch. The further from that point of parting cash you get, the chances of you making another purchase decrease. If that appetite is low, that is a "cold market". So the further you get from purchase, the colder you get, and the more work that the seller has to do to persuade a customer from part with more money.
There are some other psychological paradigms at play, for example the very common "collector" trait most of us have to one degree or another, seasonal differences (yet again), the cool of new discovery etc. All have their effect.
Marketers use a feedback mechanism, observing using measurements, the results of the actions they have taken towards their given markets.
It is not enough to think in simple terms. You need to know what works, how, when, by who, where, and the you need to know your target markets well. In the case of music this is generally your customers, your fans.
What is the available budget? Also what do current fashions dictate? 8 used to be a minimum, but these days 11 or more is more common.
It's better to have some extra songs. Anything that adds perceived value is a good thing. There are other ways to keep your list hot. For example acoustic versions of songs, live videos, an official video, video interviews, merchandise offers, live performances... the list goes on. The point is, variety helps keep them interested, keep fans buying and it allows you a good length of time for writing and recording new material (along with all your other commitments for promo, publicity, interviews, live performances etc.).
How long is a piece of string? The fact is that there are many, many factors involved in what makes a song or artist successful. Talent, songwriting skills, performance skills, image, interviewee skills, fan base, budget, connections, sponsorship, hype and the ever essential x-factor (in the traditional sense of the phrase, not the show), airtime, magazine and newspaper column inches...... and more..
More common is the fact that there is a HUGE range in the budget assigned to an A-list artist, and a B-list artists, never mind those further down the alphabet. A breakthrough single in mainstream music can cost easily more than $1M. If the single, despite it's success, doesn't make a profit, or enough profit, the record companies are less likely to spend the same level of cash on 2nd and 3rd singles to the extent they never make an album. As the budget decreases the artist also loses other A-list benefits, including A-list opportunities, including writing and production opportunities. People also do see through the illusion, or the artist isn't what they first thought, or simply because fashion has moved on and that artist was too genre specific, or their recordings and image were.
The point is there are many factors that cause sales to decrease. Choice of single goes by many factors, not just the executive's perception of "best song". It can be down to season, or some environmental factor (charity singles, public opinion, politics, events etc), an overall themed campaign, and the result of market research including focus groups.
Okay so this all sounds a long way from music, but to be successful you are well served to learn from historic approaches to selling music, movies and product marketing.
Do you need to do it all? No, but then you might spend a lifetime saying "What if?" Even worse if you have already sunk a lot of money into your music. Do you, personally, need to do it all? No, but often getting others involved costs money, and you need to know they will do it right.
There are also many levels of success. Cut your cloth according to need and capability, both artistically and related to business.
I hope this helps.
Cheers
John