It kinda depends to an extent on how far either way you vary from that date of 650 BCE. You've hit slap bang in between a couple of quite warry bits for the Spartans. The second Messenian war was 685- 668 BCE. They had a little break before embarking on more war in 645 BCE with Tegea until 560 BCE. You can't really talk about a typical Ancient Greek as different cities were very different, some were at war, others weren't, some were founding colonies, others weren't, there were democracies,oligarchies, tyrants, etc. Sparta was more rural than other cities, being more a collection of villages. Lifestyle would have been very different dependant on the social class of which you were a member. Spartiates led a very militaristic lifestyle, training from the age of seven,living in messes until thirty and unable to travel. There was a second free class called the Perioikoi who were not able to become full citizens. The perioikoi lived in semi autonomous Polis but still contributed to the Spartan Army. They could hold land, travel and unlike Spartiates they were allowed to engage in economic activity, trading, being craftsmen etc. The lives of the Perioikoi were much closer to those of greeks in many other cities than the lives of Spartiates were.
In fact, there's no evidence whatsoever that life in Sparta in 650 BC would have been any different from life in any other Greek city. Later sources liked to project the typical features of Spartan society really far back, but contemporary sources don't actually show them being in effect.
Take the Spartan poet Tyrtaios, for instance. He's supposed to be writing roughly around the time you've picked. He does not mention any part of the Spartan upbringing that we're familiar with. He does not suggest that Spartan life is different from the life of other Greeks. Are we to assume that he just kind of glossed over everything that made the Spartans Spartan? Even though he was supposed to be writing their battle hymns?
It's notable that in the early 7th century BC there are still loads of statuettes being dedicated at temples in Spartan territory. This shows that the Spartans did not yet have any rule forbidding displays of wealth. And a lot of those little figures are archers, not hoplites like Spartan citizens were later all to become.
In short, daily life for a Spartan citizen in 650 BC is likely to have been more or less the same as the daily life of the Messenians he was fighting. It's not until more than a century later that we're beginning to see some features of "Spartan" Sparta.
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