Don't use a task manager, apparently Android is very good at managing running tasks and it just causes problems. I tried using one and a few things stopped working, uninstalled and won't be using again.
The first app you should get is called AppBrain. Download that, then head over to
www.appbrain.com. There you will be able to browse the market online, select what you want to download etc. Then go to AppBrain app on your phone, select manage my apps and then sync. It'll then go through each install/uninstall one by one, including updates.
Other apps I use a lot:
Astro File Explorer - a good tool to view files/folders on your phone.
Battery time lite - easy to see how much battery you have left. If you set it up you can have a % in your task bar.
Where's my droid - allows you to set up a code phrase to text your phone when you misplace it. It'll ring the phone even if it is on silent.
UK TV droid - TV guide, can setup reminders for programmes (freeview only I think).
Handcent - alternative sms client. I like it because it gives me a quick reply pop up to every message received and can also change the LED notification colour and frequency (I set it to flash until I read the message).
Google goggles - can take pictures of foreign language and will auto-translate, or landmarks to find where you are. Also has a barcode scanner bult in for price comparison shizzle.
Pkt Auctions Ebay - Ebay app.
Google voice search - might be installed already.
Paypal - manage your account.
All those are free, I don't like paying for things. If you do pay for an app and it's shit though, if you uninstall within 24 hours you get a refund.
There are plenty of other tweaks you can do, depends what you're after really. Phandroid is probably a good place to head to, xda can be a bit involved (custom software roms etc).
Oh and an update to Android is expected this quarter for the HTC Desire