Hi, thanks for your great question!
According to our friends at Instapage, the average CPC for a Google Search ad is $2.41 for search network ads and only $0.59 for display network ads on the Google Display Network. 

However, when considering which strategy to go for it's not as simple as cost. 

Display ads have a low click through rate. This is because many internet users have what's known as banner blindness. They tend to expect and ignore ads that are display ads. However display ads are great for awarness and getting your product brand recognition. They may not click on your ad but you will have established brand recall. Also display ads are great for retargeting!

Search ads by contrast have a high click through rate as your ad is targeting people that search for your product or service. The other advantage to search ads is you only pay when some one clicks on your ad so even of you don't get a click through, search users will still see your product. 

Finally, if you have also used display ads previously they can associate the search ad with the previous display ad and likely click on it!
Don't be afraid to use a combination of display and search ads to ensure great brand recall and higher clicks!
It's great idea to contact a service provider such as an advertising agency to formulate a campaign strategy and implement a display AND search ad campaign in stages.