to clarify - i am a small business owner who is looking for CRM that works with Office 365 and Outlook and Sharepoint and integrates without breaking the bank. I have recently upgraded our small team to office 365 so we are now on common platform. our old system had multiple versions of office, basecamp, dropbox, i-contact ... want to find something that gives me benefits of all three, is a good basic CRM that can integrate with office 365 or allow me to drop any of above tools while enhancing any existing tools, refer leads to an outside sales team, and does not break the bank
Dynamics is Microsoft's own CRM solution which integrates seamlessly with Office 365. However, it is quite pricey with the online version starting at $44 per user per month. A nice alternative is Zoho (this is what we use), which has multiple affordable pricing plans. Zoho's capabilities include: sales force automation, sales tracking, productivity, social CRM, and mobile capabilities. Another great solution is Insightly, which is a bit more expensive than Zoho, but is powerful as well. It integrates well with Office 365 and has mobile capabilities as well. Both Zoho and Insightly have a free plan, so you can test them out and upgrade if you require more features.
As for basecamp, i don't know if they integrate directly, but there are third party websites like Zapier that will help you integrate zoho or insightly with basecamp. Zapier has a free version as well, so you can try it for free before making a decision. I personally have used basecamp on some small projects with friends and while good for project management, we ended up moving to free alternatives (nowadays there are many options, freedcamp, do.com, etc). Zoho and Insightly both should have some task management capabilities as well, so you may not need basecamp, except to import your existing projects.