There's a range of VoIP telephone devices - understanding the difference between them is a crucial step!
There's hardphones, ATAs, softphones with headsets (that you use already) and softphones with USB handsets.
Hardphones are self-contained phones. They look like traditional phones and behave like them, but they don't (usually) have a socket for a traditional phone cable. Instead, they connect to your Local Area Network through an RJ-45 network port or in some cases Wi-Fi (I wouldn't recommend this as, generally speaking, Wi-Fi and VoIP don't mix well, for reasons I won't go into here).
An ATA is an Analog Telephone Adaptor. This has an RJ-45 network port on one side, and a telephone line port on the other. You plug one end into your LAN and the other into a traditional phone. This then allows you to use your existing phone as a VoIP phone. The only downside is that some advanced VoIP features may be hard or impossible to access (place caller on hold, call transfer, do not disturb), though this is more of an issue for installations with multiple extensions. You can plug a DECT cordless phone into an ATA and use the cordless handset elsewhere in the house. This is usually the best way (in single phone installations) of getting wireless VoIP capability - DECT is designed for voice use, Wi-Fi isn't.
A softphone with headset is what you have at the moment. This uses your PC to provide the main functionality of the phone (dialling, call connection, network packet encoding and decoding) and uses an audio device to provide the speaker and microphone. If you're using a headset, you are strongly advised to use a USB headset - this has the audio hardware in a "blob" on the USB wire. This audio hardware is specifically designed for headset use, and is usually much better for this purpose than the audio hardware in your PC (which is more likely optimised for gaming). The major downside of a softphone is that the PC is part of the phone - and if the PC is doing something else that's placing demands on the CPU or network, then the phone functionality will suffer and you will get distorted or dropped calls. The advice about Wi-Fi above holds true here ... if you use your laptop and a softphone over Wi-Fi, you are introducing yet more potential for quality and reliability problems.
What I think you're looking for is a softphone with a USB handset. This is essentially exactly the same as the softphone with headset, except that instead of the microphone and speaker being in a headset, they're in something that looks like a telephone handset with a USB plug on the end. Some of these USB handsets also have telephone keypads on them, and if the softphone you're using has support for them you can dial from the USB handset just like a normal phone. The one that I've used with some success in the past is the VoIPVoice Cyberphone K. Do a Google search and you'll find outlets for it ... I've ususally bought from Amazon in the past. It's supported by SJphone and X-Lite (X-Lite 3.0 includes support for it, but with the earlier version provided by Voipfone you have to ask for the Cyberphone version on the X-Lite support forums). Others may work, but you need to check compatibility carefully - most USB handsets only work with Skype. The advice on Wi-Fi still holds true though - not to be recommended in most cases.
Softphones are a great low-cost way to start exploring VoIP, but can have reliability and performance problems. Once you start to rely on your VoIP phone you should explore a more reliable method - either an ATA or a hardphone.
In your case, I'd suggest an ATA plugged directly into your router and a DECT cordless phone basestation plugged into the ATA.