Ok, this can be the start before I head to bed and answer the rest tomorrow.
Firstly, SEO shouldn't really be offered as a standalone if you can help it. You need to understand their business as a whole. If SEO is truly the best strategy for them (they already have organic presence and a decent website that functions well then by all means - but if they've got an old, tired website that isn't going to convert they need something else)
In terms of the delivery of SEO, it needs to be split as a service. You're much more likely to get continued business in todays market by having an initial consultation period of 3 - 6 months. Within that time, your technical recommendations will be implemented, you'll have passed the 4 - 6 weeks it'd take for the domain to be indexed where it's going to be and you'll have been able to set up the framework for their full strategy over a 12 month period. You'll have identified link opportunities, found influencers, done competitor analysis and got a decent level of content written to learn from the data it provides. So if you have the ability to, 3 - 6 month initial terms are perfect. Allow your services to be taken as standalone to fit the client budget.
Technical (on-site) Link Acquisition Outreach Content Social Paid Search Analytics Competitor Analysis Conversion Rate Optimisation Link Profile Analysis Penalty Work
Do not, whatever you do - forecast rankings (ever) or agree KPI's in the first month. It won't work. You're new to their market in most cases and saying "yeah we'll increase YoY traffic by 25%" is utterly stupid. You can mutually agree these after you set out the foundations and understand their market position.
In terms of tools - I swear by SearchMetrics and AHRefs. You can do 90% of what you need to do as a small agency with them. If you're more tech focused then Deep Crawl and Screaming Frog are the best out there.
To go from small to medium? Pitch like you're a family. Play the "extension of your business" card. Focus on local. I've seen small agencies pitch for clients hundreds of miles away, only to lose out to the "local" agency, even in spite of the distant agency being much better. Focus around you and allow your name to be mentioned. Also don't be afraid to case study. Put it in your contracts that you may showcase the work and/or speak to them later about being part of your site.
Hope that helps!