I also had this question in my mind when I was looking to learn piano and guitar. The right answer to this question only depends on you. This is because if you are passionate about anything or have interest, your learning becomes easy and fun. But if you say that you have an interest in both the instruments and your passion for them is quite similar then I would say that you should start with learning the piano fast. This is because it is easy to play, learn and even an amateur person can make some initial combinations of tunes by himself without any guidance.
Learning Piano
You can start learning the piano by watching videos on YouTube and try to follow them if you want to learn some basic songs fast. Try to find good piano tutorials that start from very basics and don't just stop on any tutorial as you can get confused right in the initial stages.
Apart from that, you can take piano classes near your home or can also take online piano lessons as they are affordable and quite comprehensive. One very good online piano lessons are Piano For All by Mr. Robin Hall. You can check the review of piano for all here. The course comprises of 500 audio lessons, 9 eBooks and 200 video lessons.
You should know that piano learning is not a down the hill drill kind of a thing you need to take out some time every day in your routine to practice piano if you want to learn it efficiently. Otherwise, you will forget piano chords and will get frustrated. Try to focus on your learning.
Moreover, once you are able to learn and play the piano, you will feel good about yourself and you will be motivated to learn the guitar. This will make your guitar learning journey much easier.
Learning Guitar
Learning guitar is also fun because of its sound of strings. Now that you have learned the piano, you will learn the guitar much faster than piano. Firstly, get used to the sounds of guitar strings and also different chords. I suggest you start with the acoustic guitar as it is easy to play than the other.
Take 4-5 days to get used to strings and sounds they produce in different chords. Also, play with guitar tuning by tuning the chords and listening to what sounds strings produce during tuning. You also need to learn guitar tuning but you can also take help from an expert in your guitar tuning at initial stages.
Once you remember them in your mind, you'll will recall them and automatically know what chords to play when you'll be playing some songs on your guitar.
The next step is to start with easy to play songs. You can find many easy to play songs on the internet you just have Google. As you will start with easy songs, your progress will be much faster.
You can also do group learning with your friends and it will make your learning much easy as everyone will help each other and also there will be healthy competition in your group. Competition is always good as it motivates you to get better and better and to give your best in anything you do.
Conclusion
Start with learning piano first as it easy to learn as compared to the guitar. Once you master the piano and learn fully in a way that you can easily play songs on your piano, then is time to move on to guitar learning.
Don't switch instruments when you are halfway down in your learning. By doing this you will not be able to learn any instrument fully and you will keep jumping from one instrument to another. So, master one first, gain confidence and then move on.
Lastly, start with easy to play songs in both the instruments. This alone can make your learning fast and easy.