Which part of my turntable system should I upgrade


Hi! I'm looking to upgrade my system. I have a budget of 400$ including shipping and cables and everything else. I'd prefer new to used and/or vintage. I do have a couple ideas in my mind, but I'm not quite sure and I was wondering if anyone here had suggestions/ideas!

I still haven't figured out what "bright" and "warm" sound like so I can't comment in that respect, but I listen to a lot of pop punk/indie punk (Broadway Calls, The Menzingers, Sundials, Junior Battles, etc. -- I think their stuff's on YouTube) and also a few acoustic bands. All of my music is from the past 10-15 years.

Turntable: Denon DP 300F (built in phono)
Cartridge: Shure M97XE
Integrated Amp: NAD C315BEE
Speakers: Wharfedale Evo 2-8

The Denon has been weird ever since I got it (I bought it used online, and it plays noticeably faster than it's supposed to, I checked with a strobe light but don't know what the problem is --- I even replaced the belt) so I'm thinking about replacing it. On the other hand, I love the automatic feature, and I can't think of another budget turntable on the market that has it. I like to fall asleep to records, and the auto-stop feature is great. I'm also not very adept at placing the needle on the record, and that's where the auto-start comes in.

When I originally bought my system, I had a Denon DL-110 but a friend bought it off me and I put the Shure in instead. I was also thinking of upgrading the cartridge (to a Denon) and then I'd have $260 left over to spend.

I"m not sure how much the built in phono is impacting my system. I live in an apartment with my parents so adding an extra piece to my system will be a hassle, but if it'll make the biggest difference, I'd definitely consider it.

I was also wondering (since I'm not much of an audiophile) if there are any parts of my system that's out of balance quality-wise? i.e. the speakers are too good for the turntable, or the cartridge is subpar compared to the rest of the system, etc.

On a final note, minimal manual installation/effort is a huge priority for me.

Thank you so much! I appreciate any and all feedback :)
toxicwaterfront
adding a nice tube phono stage would make the vinyl sing.

Bottlehead Seduction, Hagerman Comete, Project Tube box
...why would you want a phono stage.....there is room for improvement is all of your components. I would not change a thing until you have sufficient funds to take a giant step. If your NAD has a headphone connection, I would try decent cans which will give you better solo sound.
Your Denon might be running fast if it was intended for a different country. Check to see what voltage and hertz it was made for.

The weakest part is probably the built in phono preamp.