As Hc4361 indicates, you only need a wifi connection (and a relevant subscription) to watch the services offered by Now TV. However you need to remember that those services are designed to
supplement Freeview channels. Those Freeview channels (such as BBC1, ITV1, C4, Dave, Drama, etc) aren't streamed to a Now TV box, so you can't watch them without an aerial.
What you'll get with a Now TV box without a subscription is catch-up services (such as BBC iPlayer, ITV Hub, All 4 and Demand 5) plus the ability to view Youtube videos on your telly and various other services, as per this list:
http://web.static.nowtv.com/email-marketing/assets/legals/NOW_TV_apps_21AUG2015.pdf
An Entertainment Pass costs £6.99 per month (with no contract) and gets you Sky1, Sky Arts, Sky Atlantic, Sky Living, Nat Geo Wild, Gold, Comedy Central, Fox, MTV & ITV Encore. It also gives you access to a some box sets of programmes.
A Sky Cinema Pass costs £9.99 per month (again without a contract), giving you access to over 1000 movies.
A Sky Sports Pass gives you access to all of Sky's sports output (except for pay-per-view events, such as world championship boxing matches). You can pay £6.99 per day (possibly worthwhile if there's just one big event you want to watch), £10.99 per week (handy for Test Match cricket) or £33.99 per month.
For completeness, I'll mention that there's also a Kids' Pass (with thousands of children's programmes available) for £2.99 per month.