Single-engine plane with long range flyable in Europe Not 100% sure if choice of airplane is on-topic here, please let me know if not.
Just got my PPL, and looking for a choice of single-engine meeting a few conditions:

Long-range, definitely &gt;800nm, ideally &gt;1200nm
Can be flown IFR with only IR (no special type/class ratings) under both FAA and EASA
Available used for under $100K, ideally less

Are there planes out there that meet these conditions?
There are definitely aircraft which meet some of your criteria, namely range above 800nm and can be flown IFR. I'm not going to list them all, notable examples would be the Mooney M20 series, the Cirrus SR22, Cessna 182 and Cessna 210. No doubt there are more. The issue will be cost, you can find older M20s and Cessnas for your budget, the cheaper they are the shorter time the engines have until they need a costly overhaul and the more work they'll need.