Welcome.
First question
Do you really want to play piano or a keyboard?
A piano will have 88 keys and a heavier action to the keys and piano playing will develop along playing Bass lines with your left and the treble or melody lines with the right.
To play true classical then it is piano but to play a classical piece when you have learned to play a keyboard is more akin to playing it in the style of.
A beginners keyboard is probably an arranger type intended to have chords played left handed and the melody line with the right hand all whilst auto accompaniment is taking place where the accompaniment is triggered by the Style chosen and the actual chords played. Do note that a pro musician in a band will not play their keyboard like this, more likely chord variations in right with chord bass not and harmonic with the left.
Onto keyboard within and above budget.
Yamaha PSR E 363 is $199 but in all honesty it is not very good, the sound is only so so, the build quality is not the best. I have played one as recently as 6 weeks ago and wish I had not.
Casio CTX 700 at $175 is a much superior keyboard to the Yamaha but at this price point it will have limitations.
A bit more in cost but much superior is the Casio CTX3000 which is $300
Yamaha has their PSR E 463 which is also $300 the downside is that the menu system is the same as the 363 as is the build but there are more available sounds and styles.
My advice is to consider the above, look at them in store and compare them, the sales person will be keen to help.
What I suggest is up your budget and buy a more quality keyboard like:-
Yamaha PSR EW 410 at c$430
Roland Go Keys or Go Piano both priced at $330
Korg EK 50 c$400
Or
If you decide on a digital piano
Yamaha P45
Roland. FP10
Korg B2
All of these are c$500
Yes I have gone way over budget and with that I wish to guide you into choosing the best keyboard to learn on that you will not soon outgrow which you will with a $200 keyboard
The way I see it is that people buy a low cost keyboard and are keen initially but then the sheer button and menu fiddling required to go from one style to another which together with the fact that the keybeds are not of the best quality then disillusionment steps in and the keyboard is consigned to a dark corner.
Hence buy once but buy wisely.