£2k for what you have described is reasonable. However, I would be factoring into that an email campaign and remarketing.
You are going to be spending a fair amount per click to get people to the site, either via social or GAds, so its key that you get those people into a remarketing audience so they keep your brand name in their minds and are hit with some ads after they have left the site. Especially important with a product such as yours where the decision to pull the trigger might be more likely after a few vinos on a Friday night!
As a side note, If the site relates to gambling, you will need to show google and FB various licenses and jump through a few hoops before you get up and running.
Key things, especially with FB/Insta, is to segment your Ads, and analyse it like a hawk. Start broad with the audience, and split test your ads.
So for example.... you might want to start by targeting 20+50 year old with 4 ads, targeting professionals and blue collar (for example). Let the ads run, and then dig into which ads perform best, and which segments of the audience engage with them. Narrow the audience down, and as it rolls your cost per click will come down as you start to remove the waste.
Always have 2 ads per campaign minimum, and continue to remove the weaker performer, so performance doesn't dip. Dont expect the same click thrus in month one, as you'll get in month 3,4...5 etc.
Important.... don't have too many campaigns for your £2k budget, or you'll end up with so little data (exposure) per campaign, that you cant make sensible judgments on how to improve.
Hope that helps
