Semantics are a big challenge when implementing any system and this is one of those little challenges that you see all the time. The same word is used in many different places to mean many different things, or different words are used in different places to represent the same thing. This issue is particularly pronounced when you're working with Salesforce.com ("What do you mean a contact IS a lead?")
Engaged and Influenced really represent the same thing - We did X which had the intended result that the lead did Y
One thing I've adopted as a best practice in a number of instances is replacing these values with "Achieved Marketing Outcome" - It allows me to replace Conversion (often the source of a lot of misunderstanding with demand gen and sales teams both of whom use the term to represent something different), Influenced (easily confused with "Opportunity Influence" - another SFDC features), and Engaged (used in Engagement programs and Engagement scores in Marketo). It also combines Achieved and Outcome - which helps make it very clear even to non-Marketo literate marketers that it's a good thing!
In answer to what I count as a success it generally depends on a few factors, but with standard marketing activity channels I define success as being "Any status beyond the outcome which Marketing should be held accountable to in this process". So if your nurturing programs are generating a high level of engagement - then that's what they are intended to, and should reasonably expected to do... That doesn't mean that I don't want to track to say MQL as well, but I include BOTH statuses as success because it gives the fairest evaluation of the effectiveness of an activity.
One interesting example I can offer is Webinars: Some companies react to webinars after the event date and follow up with people who attended - This is a fairly common practice because Marketo's defaut webinar program uses "Attended" as the first success status.
That said, I've also worked with companies who start following up as soon as someone registers.
Now - That's very understandable too, because we've all been there when we see an interesting sounding webinar but when the date comes around w're too busy to attend for one of a million reasons, but it doesn't change the strength of the initial expression of interest (Having monitored it in a number of instances the difference in business outcomes between registration and attendance fluctuates between about 20 and 30%).
Where this is the case and the company's process kicks off once the registration happens, I recommend that clients use "Registered" as a success, because I understand that the company's processes actually TREAT that registration as the outcome they are hoping for.
There's dozens of other examples, but I feel as though I've already taken up enough of your time. If you'd like to discuss it further feel free to reach out, I'm always happy to talk Marketo 
- Guy
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