You cant access the free trade marketplace without verified account.
The prices for SR cards usually are:
14 cost or less:regular = 1 drink or less [example:
13 cost ibuki for 1]
very limited/favorite = 5-20 drinks [example
14 cost eve for 20]
15-16 costregular = 1-2 drinks [example
15 cost kaede for 2]
very limited/favorite = 20-100 drinks [example
15 cost momoka for 45]
17-18 costregular = 1-10 drinks [example
18 cost nono for 8]
very limited/favorite = 50-400 drinks [example
18 cost anastasia for 100]
19-20 costcheap/unlimited = 25-100 drinks [example
20 cost yui for 75]
limited/favorite= 100-500 drinks [example
19 cost karen for 500]
21 costregular event ranking SR = 150-250 drinks [example
21 cost feifei for 200 (you can get the SR+ for only 300 since the nonupgraded card is cuter)]
gatcha SR = 200-600 drinks [example
21 cost nana for 400 (current gatcha)]
favorite event raking SR = 400-1000 drinks [example
21 cost arisu for 500]
There are of course lot of exceptions where lower cost (17-20) card can be even 1000 drinks and also some very cheap 20 costs for like 15.
In the higher costs the prices vary a lot based on sometimes unknown factors and also change quite often. For example the 20 cost yui I mentioned above was one of the very last gatcha 20 costs before it switched to 21 costs, and so she dropped from 500 to like 75 current price.
Some stat factors deciding how much a card costs are whether the card has more attack than def, whether it has an attack buff (generally anything with def and def buff is bad and hence super cheap), whether the buff is random (so only buffs some people) or full (buffs everyone) etc.
Some art factors deciding how much a card costs are voice, swimsuit/summer dress, wedding dress.
And well the difference between being verified and not is that you can trade, enter special campaigns, receive daily bonuses for logging in and use friendship points to level up idols. Without trading you are pretty much locked to RNG what you get and earn yourself which is pretty bad if you like particular type of idols or a specific idol in particular, since you'll have very low chance to get her (pretty much 0 without spending lot of real money). When you can trade you just trade what you get and don't want for the girls you want or like.