Thin command line-capable client for Linux I need to set up linux server for web service that could generate bitcoin addresses and check the balance on them, etc (basically, receive payments in BTC). And I do not want to use third-party online wallets and services.

Original bitcoind client is too large now, you need almost 20 GB just to store blockchain files, and that'd be pretty expensive even for VPS.

Are there any thin command-line linux clients for this purpose? Electrum is GUI-based (it's command-line capable, but to set it up you need GUI anyway), Multibit too.
Electrum has a thin client.  Does not need a full block chain.  

It is available as an RPM for Fedora which will run on Centos 7 =>  See https://www.rpmfind.net/linux/rpm2html/search.php?query=electrum  and the Rawhide version is the latest which will run on Centos 7 - you will need to source out and install dependencies one at a time as it complains they are missing and retry until it intalls.  

See also http://docs.electrum.org/en/latest/merchant.html  It will run command line as a daemon or you can set up Remote X access with Qt but as stated by ThomasV it can be used completely command line who would know best of all.

You will need to open the ports needed 7777 and 9999 in the firewall and once you launch it issue a =>  netstat -anp | grep 7777 to make sure it is listening

Then do => electrum daemon load_wallet

Do =>  electrum -h - to see all the commands available from the command line of via a curl call.  See the link at the bottom for more on curl calls with software like PHP or website webstores

However if you leave it running as launched from the shell it is likely to die so . . . then set it up to start on boot and respawn if it fails

And the service file, in /etc/systemd/system/electrum.service:

[Unit]

Description=Electrum Bitcoin thin client

After=network.target

[Service]

Type=forking

User={USER}

Restart=on-failure

ExecStart=/usr/bin/electrum daemon start

[Install]

WantedBy=multi-user.target

Assuming above you change the "User" to  &lt;= whoever you will run it as and assuming you installed the rpm - the path to electrum is then correct as the path.  Enabling that with => systemctl enable electrum &lt;= (on Centos 7) will make sure Electrum always starts on boot.  You will need to load the wallet manually if it fails and restarts or you reboot however.  

see also Checking/polling a balance of an address in Electrum via the command line/RPC