I've had a Futaba 3PK for bashing a few vehicles. Suddenly I am looking at getting involved in carpet racing at a new track. Should I upgrade from this 10 year old technology?
I want to run VTA, 2wd SCT, Tamiya Euro Truck and a 1/10 buggy.
Should I get a new radio and receivers? Let's say my total budget is $300 for TX and RX's, what would you get?
Budget of $500?
Budget of $800?
Will a pricier setup help as a novice racer?

I would say Sanwa or Futaba. The Sanwa MTS and Futaba 4PM are great mid tier radios, I personally have run Futaba since the 80's, I find lately though that their CS is not the most helpful, and not fully up to speed with the end user. My son runs Sanwa and the speed alone of his system is so impressive. both systems run any of the latest and greatest servos.

hands down the Noble nb4, super quality radio and performance. i went from a m12s to the noble nb4 the quality feel in the hand is so much nicer.
cheap as micro rx too.

I really see no reason to upgrade. I still have 2 of these 3PK's and wouldn't part with them . They do all I want and then some. Use one for carpet oval cars and the other for my Dirt trucks. Use a 3S Lipo and charge them twice a year.

Your 3PK has 2.4GHz FASST receivers?
If so, you can check if your receivers are compatible with the 7PX. If so then you can save some money on receivers and keep the 3PK as spare,

3PK user here. Is everything still function properly? I mean all the pots are still in good condition and has no oscillation? If so I don't see a reason to upgrade.
Still, I've got Flysky NB4 recently and it's a step up in term of response (I ran Spektrum module in my 3PK). Apart from that, not much. NB4 has almost the same control layout as 3PK too with 2 dials on the grip so it's very easy to get used to.

By the way what module and receiver you are using? If you use something like FASST it might work with newer Futaba so you don't have to buy new receivers for your entire fleet.

The 603FF and 603FS do not work with the 4PX or 7PX, I know because I was pretty disappointed when I upgraded. If you really like a drop wheel, you could go with a used 4PX. I had a 4PLS for a while and saw no issue with it, I just got a good deal on a 4PX.

There are tons of things to consider when selecting a radio, worth a read here:
Which surface radio system is the best?

As for me, I am extremely pleased with my 3 year old Graupner X-8E, this is the only brand that I know which offers a 2 year warranty, plus replacement Rx's are around $30.

Key features that are most important to me are:
1) Steering speed, absolute must have, many budget systems lack this feature
2) Drop down steering, I prefer to have the steering wheel aligned with the throttle trigger
3) Adjustable ergos
4) Easy to navigate menu

I have bounced around between over a dozen budget brands of radios as well as the following name brands and here is my personal order of preference for a mid-range system of the brands that I have personally owned:

1) Graupner
2) Sanwa
3) KO Propo
4) Radiopost

I have also tested Futaba (not actually owned one) and feel they are a wash with Sanwa, Graupner rises to the top of my list because they offer more features for the price for a mid-range system over anyone else. I also find that Graupner is the easiest to navigate with their color touch screen, not many mid-grade systems offer this feature.

What receivers are you currently running?

Definitely need to make sure your RX's support the following limitations to the 4PM:
T-FHSS SR
T-FHSS
S-FHSS

I believe the 3PK used FASST which may not be compatible with the 4PM

*** I am not a Futaba expert but I can be wrong, the main reason I have chosen to stay away from Futaba is because they don't make any of their stuff backward compatible.

From the 7PX manual: