Criticism - I hope it was a small amp. The 300/400 are nothing like the 500.
I don't own the 300, but if I remember correctly, this isn't an expression pedal. It is a dedicated volume/wah pedal. Whereas, the 500 had the expression pedal - it could control anything assigned to it.
Beyond that -
The ultimate answer is; do what you gotta do to get the sound you need to get. For example, my old rig lasted me 20+ years. I ran no loops, everything ran in a straight line, and went into the front of the amp. People tried telling me my wah needed to go here and my distortion needed to go here and put this cord here so that it bypasses this and that... to which I say "I hope you have your diaper on. You may want to take a step back, because I am about to make you lollipop your pants. And when I am done, I'm going to take your girlfriend for a test drive."
However, amp modelers are designed to replace amps. That is their purpose. You will never get a Fender tone from a modeler when using a Marshall amp. It doesn't mean you can't make it sound good, it just means that X going into Y isn't the same as X by itself.
So, yes, headphones (not $20 earbuds, not $200 Beats, we mean monitoring headphones) or a powered speaker will allow you to hear the device as intended.
I have a multitude of resources available to me. So, at home (or on the bus, hotel room, etc) I am a little less concerned with being perfect. But I run a pair of JBL Eons. I also have Peavey KB/A amps. All very good options. Not as good of an option, but totally doable - those cheap $20 computer speakers you buy at the dollar store.
Basically, anything that you can plug in your record player and get good clear tone at decent volumes is what you want. Some headphones and speakers add "bass reflex". You don't want that. If you want bass in your tone, you add it in your EQ.
But, here's the kicker -
Whatever way you decide to go, that is the way you have to go. You can't design a hundred patches using "Method 1", and then think that you switch to "Method 2". Tone won't transfer from one to the other. And there is no "rule of thumb" that you could, let's say, add "EQ Setting A" on all of your patches while using "Method 2". Each patch would need redesigned from scratch if you need the same tone.