Let's get the obvious out of the way, and those that I tried with my MZ-NH600D: All funds in USD.
Koss Porta Pro / 2 - I didn't think they were that mindblowing, even for a $40 phone. You might dig them, and they get very portable. $40USD.
Senn PX100/200 - Former's open, latter is closed. Very good for money and very portable. I'd recommend this with very small reservation. $50USD at your local HiFi store. There is a Noise Cancelling version of these, the PX250 at $150, but I don't believe they are well liked here. Your father/dad/pops is probably thinking of these undoubtly. I'd take these over the Porta Pros any day of the week.
Sony EX71 in canal phones. More than half the folks here hate them, but they never bothered to burn them in. I'll take these over Porta Pros any day of the week.
Shure E2c, E3c, ETY ER6s. ER4s are all IEMs, they block out tons of noise and offer better sound and clarity at higher prices. Unless you have small ears like I do, you might do well to start with Shure E2s or ER-6s and start from there. Starts from $100 (or lower) and up. For the record, I have Shure E3 and they are quite efficient. Same thing for the E2. Less Bass, more Vocals than other phones here. E2s though have more bass than E3s.
Getting not as portable are other phones, the MDR-V6 (NOT V600!!! They are the SPAWN Of SATAN!) offers good isolation and sound for the money, $60-80 these days. I think the reaction on these are split like the EX71s, and out of the box, they sound similarly screechy and harsh. They need burn in as well.
I'm sure there will be offers of Grados, Audio Technicas, and what not. Again, these all I've tried with my 600D unit, and with probable exception of MDR-V6, your MZNH1, if and when it arrives, should drive them easily.