Firstly, forgive me my English .

Recently I got very important and small massage. I was connected to very slow public wifi network. Unfortunately on my mailbox (gmail) was also a really big massage (20MB) and kmail was downloading it in first order. I was forced to wait until it's downloaded, to check the small message. It was quite ridiculous.

Is there any possibility to chose witch massages should be downloaded from mailbox?

There is no straight forward method I'm afraid, at least not to my knowledge. But what you could do is to set up a filter in your gmail account which will archive (skipping the inbox) all messages with attachments and apply a label to them.
Next time before you will go "mobile" you can simply unsubscribe from that label/folder in KMail and so all emails with attachments will stay on gmail servers until you won't subscribe to them again.

Alternately, set it to only download headers, which will be enough to show the subject, sender, etc. when you open the email, KMail will then download the message in full.

bcooksley wrote:Alternately, set it to only download headers, which will be enough to show the subject, sender, etc. when you open the email, KMail will then download the message in full.

Headers... neat and simple! Note to self: don't try to solve problems at night with the glass of red in your hand.

bcooksley wrote:Alternately, set it to only download headers, which will be enough to show the subject, sender, etc. when you open the email, KMail will then download the message in full.

How/where can I do it? Kmail has so many options and I don't know where to find this one.

You will usually find this in KMail > Settings > Configure KMail > Accounts > Receiving > (POP3 Account). I couldn't find it in KMail2 though... I am sure it was in KMail1 however.