You'd be best getting the 3-zone day ticket thats valid for 24h, like poster above suggested. You'll be covered for trams, metro and ferry as well if you decide to hop over to Suomenlinna. It being October tho weather mightnt be best suited for it, but play it by ear.
Tickets cannot be bought on board train itself, but there are ticket machines on platforms. Easiest by country mile is to get the HSL app on your phone, route planner on that is pretty decent as well as obvs being handy way to buy said ticket.