Kara,
You need to build this into Marketo as a Lead Lifecycle Program and MQL flow. Your website can feed Marketo leads and then Marketo's logic decides whom to send over.
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Anonymous
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Engaged/Named
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MQL - threshold by Score
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MQL - Fast Tracked (form based or other conditions)
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SQL
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SAL
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Opp
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Won
And so on. But the key is to get the MQL flows setup based on target audience and behavioral triggers. The Sync to SFDC step Kenny mentions is part of that process and does auto sync the leads immediately. Remember that implicit syncs also work like Add to SFDC Campaign and Change Owner.