If I want to perform to my family with a microphone, what equipment should I have at least? My voice is not loud compared to the piano, and I also want to add some effects to my voice such as reverb, echo, chorus etc.
Of course I need to have a microphone and a stand. And what else? Can a computer do the rest of the work, how? Do I need to have an interface like focusrite 2i2? (because I am considering to buy it)
As a rule: if you are interested solely in performing live (and not recording) a computer interface is not the best choice.
What you'll need
In order to amplify your voice you need the following pieces of gear:
Let's start at the end. A power amplifier is necessary to provide sufficient current to induce motive force in the speakers. You want at least a decent pair of hifi speakers to convey your voice with sufficient volume and clarity (assuming you will be accompanying your voice solely with a piano in a fairly small space - such as a living room). A hifi system with AUX inputs may suffice for this purpose (I've also had good results with a 2.1 home cinema system driving a pair of hifi speakers).
This leaves the matter of the mic preamp and effects processor.
Why using your computer isn't the best idea
You could concievably use an audio interface - such as the Focusrite 2i2 - to accept your microphone input, route it to the computer, apply software effects and send the processed signal to your power amp. This may be a suboptimal solution, however.
When working with digital audio, the following things must happen:
Each of these steps takes time. This introduces what we call latency - a (hopefully) brief pause between the moment you produce the original signal (that is: sing) and the moment the processed sound is heard through the speakers. The bigger the latency, the more noticeable it becomes and many musicians find that this has a negative impact on their performance (you are hearing yourself singing with a noticeable delay).
How much latency you get depends on both the interface and your computer.
Every time your audio interface receives an analogue signal, it stores the converted digital data in a short-term memory storage known as a buffer. The bigger the buffer, the more time is needed to fill it (and hence the bigger the latency).
The way to reduce latency (given the equipment you're working with) is to reduce buffer size. Unfortunately, this may mean that your computer isn't done processing the sound converted previously (because it's doing a whole host of other things at the same time) when the newly filled buffer is ready. This results in audio glitches and possibly dropouts (moments when the audio engine gives up, because it is unable to cope with the load).
Dedicated audio processing hardware (such as a digital effects processor) copes with this by being specialised - its digital components do nothing but process audio and their architecture is specifically designed for their function. For this reason, the latency of dedicated audio processing hardware is negligible.
A simple solution
The simplest (and cheapest) solution for your particular use case would be a small mixer with onboard effects. The Behringer 1002FX is an example, but there are many comparable offerings from various manufacturers. Such a mixer will provide you with a mic preamp, an effects processor and the ability to feed additional signals to it. It can be connected to any power amplifier that accepts stereo signals (even a hifi system, as mentioned above). You can also find small-format mixers with both digital effects and USB connectivity (meaning you have a recording option, as well); although dedicated USB recording interfaces will probably work better in this application.
What if you don't have anything to plug it into?
If you don't already have an amplification stage adequate to your needs (no hifi you can plug into, not enough volume etc.) you will need to get a small PA system, which - at minimum - consists of a power amplifier and matching speakers. Unless you already have a mixer, or other microphone preamplifier (and effects processor), your system would also need to provide these facilities. In this case, I would recommend getting a powered mixer (which provides a mixer and power amplifier in one unit) with speakers. Such systems often come with built in digital effects processors, these days.
This option is more expensive and is generally intended for larger scale performances (depending on the system's power), so it may be too much for your needs.
If you are just performing for your family and they have a stereo system in the same room as the piano, you might consider plugging your microphone into that stereo system, although you won't get the effects. The effects you mention are standard on many small amps (such as the Roland Cube) so you might consider getting one of those and plugging your mic directly in.
