Is there a rule of thumb that can be used for staff planning in terms of how large % of an online marketing budget that should be allocated towards managing the online marketing activities?
It really depends on your market. If you are going after a huge market, you could spend millions chasing a very small percentage of the market.
If you're going for a small/niche market, my rule of thumb is to start with a really small budget and stick to one advertising platform like Google Ads or Facebook Ads. You'll quickly find out which campaigns are generating revenue. Then start to scale them and begin testing different ad variations, landing pages, etc... After you have conquered one platform, try another platform. Rinse & repeat.
If you really want to challenge your marketing team. Give them no budget and tell them to come up with a creative marketing strategy. Half.com was able to get a city to rename itself to Half.com and generated a lot of PR.
The short answer: 0% The best thing to do is use the free power of Internet to do all your marketing. You can use countless third party services for free (or pay for them) to help drive customers to your startup.
My personal belief is that in a startup (web especially), you need one amazing inbound marketer that is great at building a community around your product. Look for someone who has thousands of Facebook friends and Twitter followers and a popular and well written blog.
Your developers should also be able to communicate reasonably well so they can contribute blog articles and attend the chat conversations as well.
Never spend more than what you can afford to lose to gain a new customer. At least concerning programs like Adwords, I would recommend spending enough to get a statistically relevant sample of your costs in acquiring the new customer, then comparing that to your profits off the new customer. If you don't profit, then don't do it. If you do profit then expand your budget until you flood out your market.
I would approach inbound marketing the same way. If you can attribute enough sales to your inbound marketer to justify their salary then by all means hire as many inbound marketers as you can handle and still profit. If inbound marketing doesn't work for you then hire a part time intern to manage your facebook and twitter pages to keep up with your company profile and leave it at that.
As a business owner your focus should be profitable activities. If a strategy doesn't work, then simply don't do it. There's enough online marketing methods that you shouldn't feel compelled to try to make a single one work for your business when others might be better. Don't let the buzzwords and trends of the moment overwhelm your good sense in what works for your business.