Any specific tools and list? Does it make sense to outsource to the third party as we have a very small sale team?
Best way to start an outbound campaign is cold emailing and cold calling. Every company (small or mid-sized) has their own revenue target at the end of the year. If you have a small sales team, then IMO, you should outsource your sales development process and let your sales team focus on closing the deals.
You can contact me at firstname.lastname@example.org or visit www.marketjoy.com to get a free demo. Feed your sales pipeline with sales-ready prospects and let your AEs close the sales deals.
Don't do an outbound marketing campaign to directly promote your agency. Instead, create great content that would be useful to someone trying to select a web/mobile development agency—such as what to look for, what you should be prepared to tell them, how to work with them, etc. Then, use outbound marketing to promote this information and get it out into their hands.
I would highly recommend connecting with someone who has experience here to shorten your learning curve if this is not what you do.
For our agency, we spent a lot of time & money outlining and creating the infrastructure which now is mainly on autopilot for our outbound strategy. For example, we now have a small team running it while sending on average 5-10k emails per month consistently. I can help outline how to do the same thing as well.
Team-wise I would lean in the direction of learning the framework, building a small team and launching some base campaigns internally. I have looked and hired a lot of 3rd party companies that claim to handle all your outbound campaigns but most are 5/10 quality wise and charge a hefty premium.
Once you know the structure it mainly comes down to team building, having a quality product/service, and creating value through very personal outreach campaigns.
Resources wise- there are some great books out there on this. I would highly recommend "The Ultimate Sales Machine" by Chet Holmes and "Predictable Revenue" by Aaron Ross. These both will give you a lot of higher level ideas and ways to structure your outbound campaigns. A lot comes down to your internal resources and budget as well.
Hope this helps!