help me to setup this site style

I am currently building a website and I need some advices.

The site has 4 major sections “SERVICES”, “FOOD”, “TRAVEL”, “PRODUCTS”.

Each section has some categories, for example “SERVICES” has
“BEAUTY” which has sub categories “MANICURE”, “SPA”, … etc…
“EDUCATION” which has sub categories “SCHOOL”, “COLLEGE”… etc….
“HOBBY” which has sub categories “SPORTS”, “DANCE”… etc…

When the page loads it displays all items but on the left it allows the user to select a specific category “BEAUTY” (which include all subcategories) or select a specific subcategory i.e. “DANCE”.

When a category or sub category selected it automatically filters and selects all relative offers.
Actually for 3 categories “SERVICES”, “FOOD” and “PRODUCTS” only one category must be selected (one radio button). The section “TRAVEL” has 3 selections.

1) DESTINATION: LOCAL / INTERNATIONAL
2) NUMBER OF PEOPLE: 2 / 3 / 4 / 5 / 6+
3) NUMBER OF DAYS: 1 / 2 / 3 / 4 / 5 / 6 / 7+

so I need 3 radio buttons/selections at the same time only for this section.

Can you please tell me in a short how can I build this in WordPress? Even if I have to use a commercial plugin, I don’t mind. I just want the right/best way.

Thank you!