Flooring Tile - cement floor-what underlayment

i removed vinyl sheeting and have cement floor left. i would like to put ceramic tile down or sheet vinyl(what is better over cement?). what kind of underlay ment should i use? if i go with the vinly do i use plywood? one more question could i have put plywood down on the old vinyl sheet and put the ceramic tile over that? if i go with ceramic tile over the cement what kind of under layment do i use?

No underlayment needed under ceramic that is going over a cement floor. Use a quality modified thinset.
Make sure there are no sealers, paints or cracks in the floor and remove all the vinyl adhesive from the cement with a scraper and hot water.
If putting new vinyl instead, I dont know what would be needed, my guess is no underlayment there either

what is the best leveler plywood or a liquid leveler?

No plywood over a slab. An unsealed slab is one of the best substrates you could have for tile. The vinyl is gone but what's left? Any glue residue? Vinyl backing? Ceramic only needs flat, not level. If the slab is flat, you are ok. Any cracks in the slab or control joints cut in it?

there is one little crack in the cement. i guess i need fracture membran for that? also i have some little holes where the carpet stripps were on one section of the cement. what can i use to fill the little holes? about 1/4 inch deep.i took all the vinly and backing and nothing left. i do not know if it is sealed. how do i tell? substracts means underlayment?

The substrate is the bonding surface for the tile, in your case, a slab. You will need to use an anti fracture membrane over the crack. This crack is all in the same plane, meaning one side is not higher than the other, right? As for determining if the slab is sealed or not, place some water on the slab. If it soaks in, you're good. If you used a solvent to clean the adhesive off the slab, you could be in trouble and if any areas are painted, that would need to be removed mechanicly first. Small divots from the carpet tack removal can be filled with thinset.

thank you for the information. yes the crack is on the same plane. how deep should i go as far as the thinset is concern? i have one little hole that is about one inch deep.is there a limit for the dept of the hole for the thinset? i use ivory dish washing soap to get the backing of the vinyl up. is this considered a solvent? i think i got all of the soap up.

No it isn't as long as it's rinsed well. I'd go over it with some clean water and a stiff scrub brush and suck up the mess with a shop vac to be safe. Once it's dry, do a water check to make sure the water absorbs. As for the holes, there are also patching compounds, portland based you can use, but I think you'd be fine to patch them with thinset. If they're 1" in diameter and 1" deep, use the patching compound or fill in two fills with thinset. As for the crack, you can apply a membrane to the entire floor or spot treat the crack. Most spot treatments will require the anti fracture membrane to be 1 1/2 to 2 tile widths past the crack on either side.

thank you- as far as the water spot check is concern-when i first put the water down it forms a puddle. than after 5 minutes i sweep the remainging waster away and the cement is a little damp. so i believe it is soaking in right?