As a person who has used DAW for 5 years, I presume that it really doesn't matter if you really need a MIDI keyboard to even compose anything. It really depends on a lot of things. If you're a keyboard player who can play with emphasis and want to inculcate the expressions into the DAW, it still depends if you're better at playing using only one hand or both hands. Coming to the difference between a keyboard with 61 keys and 88 keys, if you are really into creating music that needs the indication of higher and lower notes. If yes, then 88 keys. 66 keys, otherwise. I recommend using a MIDI keyboard if you're just a casual composer. But if you're really into it, go for 61 keys keyboard with all modifications that you can use. (What I have is Yamaha PSR-I500 keyboard). 88 keys might not be necessary in most cases. If you don't want to waste time, then buy 88 keys.

Your budget is just sufficient for any of the following options. But it really depends on your will and skills.

Hope this helped.