continuing on the discussion - i agree with oatnet. You have two real choices.
Do i do it with good batteries, or do i go as cheap as humanly possible.
SLA would be my first port of call.
They are cheap enough not to matter. ( i got 36v 17ah for $150 AU ) inc chargers by getting jump start battery packs on sale.
I will also be buying a 72v 25-30ah LiPo4 setup as well - just not yet.
that was for the following reasons:
1. I wanted two battery packs - so that i could use one for commuting and one as a "neighbourhood" pack - ie for a quick spurt to the shops cheeply, or to a friend's place, or out to dinner (only need a 20k range - i'm going to need to add one more 12v 17ah battery to get that most likely).
2. They were so cheap (4x jump start kits are approximately two tanks of petrol here!!)
3. If i don't end up using them for the bike, i will wire them in series and use them for my solar / wind generator i'm going to be buying next! - good deep cycle SLA batteries have LOTS of uses around the house

4. It will allow me to test the bike out and fix any issues that arise without the burden of the expensive pack. I want to be able to grab that pack and start DAILY commuting 60km.
There's some things to think about.
my thoughts on your situation are:
depending on your fitness level - i would suggest you consider just riding the 10miles yourself without electric assistance (if possible). The long climb you can always walk up until you're fit enough.
if you're not fit enough (or have a medical condition) thats cool, then you need to decide if you want to go as cheep as possible on the bike, or as light as possible, and develop your fitness slowly using electric assist when required. I'm unfit (for me) and rode to uni gently yesterday (50k round trip) to drop an assignemnt off, i still managed to maintain about 25kph average (inc hills traffic lights etc)
Your speeds that you want to achieve are low in comparison to others here - this is good, your power requirements will also be low
even though SLAs are heavier I'd still go them first - less risk if for some reason its not enough power, you don't like biking enough (its too cold etc) plus they can always be re-used for other projects easily ie a DIY wind generator!