Budget is 700€ music taste is broad but contains a fair swag of classical, German rock and fado.
I'll go with the Technics, but does the Denon DL_160 sound like it would be an OK choice?
the DL-160 will be a great choice.
Your budget translates to almost $1000 USD. That's a nice budget.
I would use itcro modify the SL-1200, addressing the issues most easily identified.
While the Technics torque, speed and rumble are unbeatable by any other new tables at it's price (and higher), the design remains 31+ years old.
Here is the biggest area to focus on-
The Technics stock tone arm has superior bearing specs and is smooth and of quality. But, the internal wire is nothing special, and the tone arm tube is susceptible to resonance within a certain frequency window.
To elevate the performance of this table, address the tone arm wire, dampen the tube, and also upgrade the RCA cables.
Another option is to run an alternative arm. An Origin Live modified Rega RB-250/300 is a possible choice (Origin Live addresses the uneven casting issues claimed by some of Rega arm owners, as well as replaces the plastic end stub with a metal one, and improves rear weight).
Or try a Jelco- the 250 arm and the fluid damped 750 arm are highly regarded and an easy swap (though the 750with mounting plate will be aporox. $100-$200 over your budget).
Some nifty vintage arms are a good option to consider too.
The tested resonance issues of the stock arm tube seem to be the Achilles heel - if Technics offered a Titanium nitrided or carbon fibre arm tube with dampening agent, and the M5G tone arm wire and RCAs, it'd be worth the premium.