Résumé upload functionality in Drupal 7
Add a Résumé content type. Add your text fields and a file field to this content type. Set your permissions accordingly, allowing whichever user roles you want (or anonymous) to create this content.

This will allow people to upload their resumes.

Get the Rules module and create a rule a bit like follows

Events

Node - After saving new content

Conditions

Node - Content is of type:  Résumé

Actions

System - Send mail

You can use Token to put content fields into the email, but I'm not sure if you can put links to the file.  If not, you can at least put a link to the content that contains the file.

Lastly...use Views and create a simple view that shows Résumé content -From here, get  sorted however you want.

For extra points, you could also use the Flag module to flag résumés (e.g. follow up, spam, not useful and so forth), and then create more views based on those flags (so you can only see useful résumés for exampleetc).