Okay, well you don't need the book to get access to the points, or battlefield roles.
This website is a free army builder, which has the points for every unit in Age of Sigmar.
I suggest building a 1000pt army using the points, as that'll mean both you and your opponent are on the same page (army-wise).
1000pt games are played on 4x4 tables, and you need 2+ battleline, 1-4 Leaders, 0-2 Artillery and 0-2 Beheamoths. The units battlefield roles are included on scrollbuilder. Just, ignore battleline on some troops, if it mentions a specific allegiance.
For the list. Grave Guard are very good, but expensive. I'd probably run them in two 10 man units (for flexibility) and use a large unit of skeletons as an anchor unit/tarpit. Add in other units as you desire.
I also recommend playing for objectives (even if you use 40k missions), or setting a turn limit. Most Age of Sigmar games last only 5 turns, so if you're playing the standard "kill the Most" cap the game length.
These two things in particular will make your games many times better until you get the handbook (which is amazing!)
Just remember that when building your list, you will need to (if you want) to set aside a points pool for summoning (for example, make a list for 800pts, and then leaving 200pts for summoning). You can only summon an amount of points from that pool, but can summon any number of things as long as you don't go past that points limit. It's a very flexible and powerful ability to use.