The first recommendation for search suggestions is to log and analyze all search executed on the website. The goal is to identify automatically what search is successful and failure. An example of a successful search would be if the user purchases a product or download the product marketing material. If the user attempts a search and then starts another search two minutes later we consider the 1st search a failed result. Analyzing this search history allows us to identify what search that is successful or failure. This is the approach Google uses to recommend a search suggestion and implement spell suggestions.
In addition, search suggestion needs to remember what each specific users search history and recommend search that is frequently executed by the user. If the user liked it in the past it is best to remember and offer the same suggestion. This is the same strategy a waitress at the restaurant will use if the customer orders the same items frequently. By remembering the standard order and offering what they frequently purchase at the beginning you are providing a customer-specific experience.
Next, we need to be careful to only display the right data. Show a result with products that are not relevant will cause the user to leave. To display relevant search results it is best to only display results after three characters are entered. One or two character does not give enough context to make a good guess. If some searches for "b" or "ba" we have no idea if they are searching for a bat, bathroom or bathhouse.
Another approach is to only display a select few categories on the page. My rule of thumb is to display the only top five categories. The first category will only display the top three subcategories under the first category. If you are selling products I would recommend showing the top five products. Each product should have a product image, marketing product name, short description, and user purchase price.
The final search suggestion is to only display a suggestion if the customer has access to see the product. You never want to recommend a search where no results are returned. This is important if the company will sell some products to a few customers and limit who can buy the product. Another scenario is when the company will sell the unique product for a geographic region or for a specific country. If your company limits what products are sold to each customer it is important to suggest search where the user will see at least one product.
Implementing the above steps for your search suggestion will allow you to have an excellent search experience. The above suggestions focus on providing a customer-specific experience and only display relevant data.