Just a couple of thoughts.
1. If you would like to go down the hidden field route, here are some articles that can help:
https://community.marketo.com/MarketoDiscussionDetail?id=90650000000POpAAAW see adam's explanation and comment.
Here are some additional instructions:
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Create a new form
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Add the fields you would like
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Add another field called lead source (this should exist in your instance of marketo)
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Make this a hidden field. Do this by: clicking the value
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select the input type and make it hidden (see the screenshot)
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Under the Input type, there is a field value box. Click edit settings, and write in the default value. Under that you will have to select Use Defualt Value and save it.
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Once this is saved, and is live on a webpage, it should update the leadsource automatically.
2. You can also add folks to sf campaigns that have that specific source/type. This is helpful as many people who fill out your forms may already be in your database. You can over ride their lead source each time, but that will not show the original lead source. Nor will it show all of the sources they have had. Adding them to specific campaigns can help with that. Here is a article that talks about that:
https://community.marketo.com/MarketoArticle?id=kA050000000KyqkCAC
Just a couple of ideas