First of all Congrats on the new website!
I am glad that you are serious about your marketing investment as most small businesses are more focused towards conversions no matter where they are getting from... off course PPC offer quick returns but investing heavily on PPC and ignoring organic is a worst business strategy I could ever imagine.
Anyways, in my personal opinion the budget is fair enough to start a comprehensive SEO campaign that offer REAL results and greater ROI. All you need to do is to invest it smartly!
1. Invest on Local 1<sup>st</sup>
If you are a local business (even if you are not but have a physical location) try to heir someone for local SEO submissions only!
Submitting a website to local maps, yellow pages websites and business data aggregators is a onetime game so the charges won’t be too much! If you have time you can even do it yourself by reading a blogs about how to go with local SEO.
2. On-Page SEO Audit and Implementation
With Local SEO try and find a SEO consultant who is ready to audit your website from the on-page point of view and fix the problems within the website accordingly. This will be on technical as well as on the content and design side.
**Target to achieve Local and On-Page optimization for the 1<sup>st</sup> month.
3. Social Media
This is a powerful ranking factor and can really help you lift your rankings in search engines but for a start I would advise you to start with using social media by your own and do not give it to the third party!
The major reason behind this is not only to save money but social Media is a platform where you can set your brand image in the online world so try to start by yourself as you know your business best! Later you can give your consultant to handle and manage your social media entities.
4. Link building
Now your Local and On-page is perfectly fit and you are done with your first month now hire a smart link builder to start with link building and management! I believe 2k a month for quality link building is a fine budget!
Over all your work to look in to different aspect will increase but as a result you will be able to get quality SEO services within your budget. Once you see some results started to appear in the SERPs and website started to give quality conversions... this is the time to increase your SEO budget and start with advance inbound tactics to grow audience around your brand and get 1<sup>st</sup> page rankings from the desired key phrases.
Hope this helps!