I was recently asked by a client "How should we proceed with a $10k budget to maximize signups?" This particular client is targeting a business-savvy audience, but my answer could apply to any business trying to reach a challenging and niche audience.
1. AdWords: $4k = $3k Display + $1k Search
$1k on search means we have to focus just on the strongest most relevant keywords. If you've run before, you can use some of that historical data to narrow down to just your converting and high CTR keywords. The rest of the $1k should be on trying new keywords. Don't go overboard, just try a handful of the most relevant keywords, but use broad-match to leverage the Search Terms report.
$3k for Display will be used in a three-way split between Similar Audiences (targeting sites browsed frequently by people who visit your site), standard Remarketing, and some keyword contextual targeting to discover sites with relevant and resonant content. Setting aside some of this budget for a Gmail-specific campaign may also be a good idea, as this can sometimes eclipse the rest of your spending in a contextual campaign.
2. Facebook: $3k
$1k to promote your posts. Amp up your Facebook posting. From PR mentions, to industry-related advice, to other news about what's affecting your potential customers. These are posts which can be leveraged as ads and syndicated to broader audiences. $1k on retargeting (might not use all that up if visitor audience isn't big enough). $1k on regular audience/interest-targeted ads.
3. LinkedIn: $2k
If you are targeting a B2B audience, this channel could be a big one. Start small to test the waters, see what works, then shift budget here as necessary.
4. Twitter: $1k
Also somewhat experimental, but worth trying. I'd spend all $1k to promote your tweets, not your account. If people respond to your tweets, they'll see your account. A lot of this tweet content can be duplicated from your Facebook posts (pared down to 140 char, of course). Could reach an audience that is more proactively involved in your target industry than Facebook, so there's not much danger of overlap.