Yamaha should be a good fit!
FWIW, i talked to a guy that was using a SimAudio integrated, the i-3 or i-1 or something with his Nola Boxer 1's. the Sim offers great dynamics which helped out the bottom end.
there are a lot of great used SimAudio amps on the market. they are solid, made inCanada with 20 year warranty. who offers that these days? nobody.
to be honest, I haven't listened to the Boxers, but I bet that a hybrid (tube/SS) amplifier would sound great.
Also, class D amps have come of age, so consider them as well.
I have Nola Boxer 1’s that I’ve been driving with a Creek 5350se integrated amp ($1500 in 2002, no longer available, sounds great with the Boxers but has developed reliability problems with ALPS input switch). Before I decided to go up-market I was seriously considering a Yamaha A-S801: https://www.amazon.com/dp/B00N625HZ2. New, it's +$100 your budget amount but from my research worth the stretch to pair with the Boxers. So 2nd’ing what Yogiboy said.
ps: the Boxers benefit heavily from good stands. I use Dynaudio Stand 4 (~$400) - save up and get some (or equivalent).
There is an Edge i3 Integrated Amp on USAudiomart for $600.00 great reviews and retailed new for $2000.00. https://www.usaudiomart.com/details/649447393-edge-i3-integrated-amplifier-black-free-shipping/
Full disclosure - I'm the seller of the Edge i3.
If buying new, the MF M2Si is hard to beat. Belles Aria is also a great integrated if you can find one used.
Edited to add there’s a Belles OCM-200 amp for sale right now for $595 and free shipping and it’s a great amp. It’s rated at 100wpc into 8 ohms and easily doubles to 200wpc into 4 ohms. Not mine. You could pair it with one of Schiit preamps to keep it around your budget. Worth a look.
Yamaha A-S801. Great sound and will drive those 8ohm Nola Boxers with ease. Six Moons gave it a very good review a few years ago. The A-S801 also includes a built-in dac, phono, and good headphone jack. The reverse loudness is excellent for dialing in low volume listening. Yamaha's are known for their neutral and "natural sound".
I had one for a few years, but needed a bit more muscle when I switched to larger 4 ohm speakers. The A-S801 sounded good, but couldn't get everything out of them.
Something a bit different: Nuprime IDA-8. Should be able to find one used under $1000. I have one in a second system. Great low end and details. If you have space constraints, check it out - it's small, and has digital inputs for your CD player or other digital sources.
If you can consider a separate amp and a preamp, look at the Nuforce STA 200 amplifier. $500 brand new. I haven't heard it, but it's getting lots of positive talk.
Congrats on the new speakers and the start of a new journey