I do this for a living. This is what I would do with your floor, and this would be the fastest, least expensive, least messy, most efficient approach. Depending on your access to some of the equipment and materials, you can either follow all these steps, or substitute a step here or there for something manual as required.
(Before I start, you can tile onto vinyl tiles if they are well adhered and you use a suitable adhesive, but let's assume you've set your heart on pulling them up).
1. Remove vinyl tiles (you can rent a machine which will do 15m2 in approx half an hour).
2. Sand the floor with a rotary floor machine (you can rent these) to remove / flatten the glue residue. 15m2 floor will take you 15 minutes.
3. Clear away all the tiles and vacuum the floor. 30 minutes.
4. Prime the floor with suitable acrylic primer. Drying time 30 - 60 minutes.
5. Trowel over a thin coat of SMOOTHING COMPOUND (not self leveling compound). 15m2 floor will take approx 10 minutes. Walkable in 30 minutes, can be sanded in 60 minutes, and tiling commence after 2 hours.
Why SMOOTHING COMPOUND? SLC requires 1.6kg/m2 at 1mm. It is exceedingly difficult to obtain a flat and level floor with SLC at low thicknesses. You need to be pouring it at least 10mm thick and using a spiked roller to aerate it and disperse it to every corner of the floor. If you are inexperienced and try to trowel SLC thinly you tend to end up with nothing but laitance over half the floor (all the aggregates settle in a slurry at the bottom), and lots of uneven bumps, because SLC is too runny to be hard troweled.
@ 10mm a 15m2 floor requires 240kgs of SLC. That's 12 bags.
Smoothing compound has a completely different composition and consistency and can literally be hard trowelled down to zero. An overall covering of 1 - 2mm is very easy to achieve, even if you have never used it before (just be aware you have 10 minutes working time and not one second longer, so don't mix up more than you can use!) A 15m2 room can be easily covered with 1 x 20kg bag. It also dries much faster and as you will have rented the sanding machine, you can wizz that over it to get rid of any trowel marks in the same day. In fact, you could prep the floor by lunchtime, then tile the floor and grout it in the afternoon, depending on the area involved...
Good luck Adam.