I have a landing page and I want to invest my money wisely in advertising and social media
Nowhere near enough info provided to give you advice, unfortunately.
WHAT is your service?
WHO is your target market?
WHERE is that target market?
WHY would they be interested in your service?
HOW can you monetize the value of your service for them?
Get in front of your target audience where they hang out. Give them a reason to use your service. Show them its value.
While there is very little to go by here the best tips I can provide you are:
1.Broadcast to your niche
2. Showcase the service and what makes it unique using original content
3. WHATEVER YOU DO DON'T MARKET IT AS "FREE"
The last one is super important. Even if the tool is free the market is flooded with people plugging their free tools and services. Market it as though it were paid and let them discover the added bonus that the sign up is free.
1. Find new sources to gather fresh signups
2. Create a referral program
3. Engage with people who sign up, in a way they talk about you to their network and boost your viral co-eff. This includes exciting newsletters that hit the chord.
Though there are general strategies to all of these which I assume you are aware of, for specific strategies it is important we understand what you sell and your market.