i recently wrote this for a friend who is also new to her droid, hope it helps:
k, well since i dont know much about ur likes/dislikes or phone use in general, ill give you a few basic starters that i LOVE
and ALL of these are free apps !!! none paid!
handcent sms ~ for texting ~customizing everything for messaging! different LED light colors, text sound, icon, font.. like i have one for hubby, generic for everyone else, etc.. also an option for you to have the text pop up on the screen rather than going into app to read it. (you will need to go into preloaded messaging app and disable notifications by clicking the box so that you dont receive double notifications for each text.)
they also have font packs for different fonts for the texts
Quick Profiles~ customize ringtone levels, notifications, wifi settings, etc for home, outside, bedtime, etc.. so that you arent getting woken up at 3 am with an email or whatever... you make the profiles for whatever you want, and set however you want!
my coupons~ has a WIDGET~ if u havent used widgets yet, its basically something that u put on ur home screen. tells you daily new coupons ! i use it mostly for REDBOX free movie codes
Meebo ~ if you like instant messaging, for facebook, aim, msn, all of them pretty much. but warning , if you stay logged in all day, it EATS ur battery.. so i just sign in a few times a day to see whose on FB chat, then sign out...
wheres my droid ~ u really dont ever USE this app, just nice, if u ever cant find ur phone and the ringer is on silent or vibrate, you text "wheres my droid" to your phone form someone elses, and it will make ur volue go on LOUDEST and ring for like a minute or whatver u set it for, up to 5 min i think. and also has a GPS setting incase u really cant find ur phone!
ASTRID ~ the best to do list ive found of the 4 or more that ive tried out. it also has a widget, so that u can slways see whats on ur to do list without having to open up the app.
bloo~ the Facebook app is pretty lame that comes with the phone. it doenst give u comment notifications, bloo does. cant send private messages, i use it in conjunction with the stock FB app.
sticky memo widget. ~ if u are a HUGE scatterbrain, like me ! you need to remember something real quick, open up the widget, write a note, and its a little sticky not right on ur home screen!! i LOVE this! i just set it to a 1x1 size, and it only takes up one spot, its awesome for forgetful people. lol!
Home++ (yes write it like that) its a home replacement! give you up to 7 home screens rather than only 3, and continuous loop so you can just keep going right and get back to main home rather than to the left, then back to the right... also has a power bar at the bottom~ with a phone, contacts, voice call, favorites, notifications... play aroud with it, i LOVE it
Dolphin Browser ~ more like th iphone browser, u can pinch to zoom in and out, so much bettter tha stock browser!
i used to use TASKILLER till i recently read a lot about it... its not exactly necessary.. the phone will close what it needs to close when it needs to.. i used to be pretty OCD about killing everything, now i just dont worry about it..
well, those are some core apps that for me are a must have! i go to the website androidforums.com then go to droid page, and read thru there, i have learned a lot!
and most importantly, the droid is all about being YOU! so set it up with a pretty background, put up a pretty clock... decorate it
i have a case for mine, i need a case, im a phone dropper
i got from the verizon store, its silicon, kinda rubbery, makes the phone bounce right back, lol . it can get in the way of the keyborad a tiny bit more than case-less, but i dont find it a problem..
the battery is not fantastic. you can leave data sync off, but i havent found that all that helpful.. so just plan on charging it nightly, or keeping a spare charger in ur purse..
well, that about sums it up... for now...
seriously tho ive had it for over a month, and still play around with new apps, and getting it how i want it DAILY! its fun to do