Having diffaculty installing my new HDD as a storage drive

Neither your description nor your signature indicate the case or the "front mount tray" you placed this HDD into. You're acting like it's a HOT SWAP drive bay, is it? What OS? What HDD capacity?

Does the drive show up in BIOS

That HDD is properly "in"? Hot swap bay properly connected via SATA and power? Shows up in BIOS? Is set to AHCI in BIOS?

If you are running Win 7, 2TB size is irrelevant.

Check the hot swap bay connection - there should be a thin connection running to the motherboard, and there should be a fatter flat cable running from the PSU to the bay. Both should be firmly plugged in.

The drive is there and windows sees it. You need to create and format the partition.
http://windows.microsoft.com/en-US/windows-vista/Create-and-format-a-hard-disk-partition

Windows labeling it New Volume is default. You can change the name if you want, it won't affect performance either way. As for the Healthy Partition, this is what you want to see. This means all is well. I can't really say how current operating systems handle bad sectors as I haven't had a bad sector in probably 15 years, just had drives die completely (it's very rare, mostly the become too small by the current standard and get replaced).

The recovery partition is what holds the windows recovery data from your system manufacturer. This enables their "restore to default factory settings", whatever they may call it. They do this so they don't have to ship a windows disc with the computer. Unfortunately, this will not restore any programs you've installed since you got the computer.

The system partition is what windows creates when you install it. This is where some system files reside. It's best to not mess with this partition.

The Acer partition is your C: drive. When they created this partition they gave it the name Acer instead of New Volume. Windows, Program Files and everything you have installed or copied or downloaded to the computer (before the new drive) resides on this partition.

Your new drive has been partitioned, it just has one partition on it. You partition a drive before you format it. You don't need more than one partition unless you want to break it up into smaller drives. Each partition will get it's own drive letter under My Computer. Some people like to name partitions for what they place on them (pictures, music, movies, games, recordings, etc) while others just like one large partition, the choice is yours.

Under Disk Management the diagonal lines you see on a partition just means that partition is selected. You can shrink or extend a partition size here, so if you decide to make more than one partition on your new drive, shrink the current partition to the size you want it to be and create new partition(s) in the unallocated space. Be careful though, if you shrink it smaller than your current data on it, you may lose some (never tried it myself).

A recovery partition does nothing for you here. There is no magic recovery by having a partition named recovery partition. If you're wanting some type of backup in place, I'd look into one of the RAID options that exist, or an external that backs up nightly.

Realize while you can create multiple partitions on the same physical drive, they're all on the same physical drive thus if the drive crashes all logical drives may lose data! Playing with partitions is more of a multi-BOOT configuration than an organization thing since you can create folders with the names Pictures, Videos, etc. without having to fool with Disc Management. Oh, and until Win 7, it was a PITA to reallocate partition sizes (although there were some third-party utilities available).

No reason to divide a modern drive with a modern OS into more than 1 partition (save for system partitions on the boot drive).