When you start getting serious about digital recording, you'll want to consider upgrading your gear. Each component in the signal chain adds noise to the finished product. Better quality (and therefore more expensive) gear adds less noise. Even quality cables can make a big difference.
Beyond the noise issue, higher-end hardware also gives you more flexibility in your studio. For example; need to record drums? Then you may want a multi-channel sound card. Your sound card determines how many tracks you can record at once. Typical entry-level sound cards are stereo (2 distinct channels). That means you can record 2 separate tracks at a time. If you want separate tracks for Kick, Snare, Toms, Cymbals, etc. then you'll need a multi-channel sound card.
Ask 10 people which is the best mic/preamp/monitor/sound card/whatever, and you'll get 10 different answers. But here is a short list of rather inexpensive hardware that gets a thumbs-up from almost all of us.
Microphones: The venerable Shure SM57 & SM58 are always a safe bet. Studio Projects (B1, B3, C1), Marshall Electronics (MXL 600), and Audio-Technica (check out the MB4000c) also make very nice mics for not a lot of money.
Microphone PreAmplifiers: Both the Rane MS 1b and Studio Projects VTB1 are very impressive.
Mixers: Behringer for entry-level. Mackie is a touch better.
Sound Cards: Terratec, M-Audio, and EchoAudio all make excellent, 24-bit cards. The 16-bit Creative SBLive is lower quality but very usable.
Monitor Speakers: If you're just getting started, the Radio Shack Mini's ($75 pair) are a forum favorite. You'll need a power amp to drive them (old stereo amp works great!)
Video Cards: You might consider a dual-monitor setup. If so, the Matrox G450 & G550 are highly recommended. For single monitor setups, we recommend a cheapie 2D card. Note that some gaming cards have been known to cause trouble.