Upgrading Drupal

Being asked to give a quote for upgrading the drupal core for a website I'm wondering what risks I might walk into along this project.

One of the requirements are for example:
upgrade existing drupal 6.19 website to 6.22

A good part of the site relies on 5 or 6 contrib modules like views, cck, and such. Can I expect that upgrading core will influence the interaction between these contributed modules and core or can I assume this is backported?

Thanks in advance
Undersound3

I am trying to update our website becuase the developer is charging us so high to update it when we saw the outdated version security release. I am upgrading from 6.19 to 6.22 and I have this massive error message. It started right from the last stage of the upgrade process and I thought by the time I re-enable the themes and custom/contributed module, it will be ok but alas, it keeps escalating. I am a complete newbie here. Kindly help me out.

This is at the last stage of the upgrade process. I changed the permission to 777, it does not still go off.

warning: unlink(sites/default/files/css/bef1fef5e5fb44a3ebd6517c14bc3eda.css) [function.unlink]: Permission denied in /home/myrestor/public_html/includes/file.inc on line 481.

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After enabling the themes and custom modules:
The selected file /home/myrestor/public_html/sites/default/files/tmp/fileS5y0d8 could not be uploaded, because the destination sites/default/files/css/css_7e09b9803c1651d5fdd47c9c999a1470.css is not properly configured.

warning: unlink(sites/default/files/css/css_3b3992d729bc6cb97fa60561c06d3004.css): Permission denied in /home/myrestor/public_html/includes/file.inc on line 481.
warning: unlink(sites/default/files/css/css_e5c04d204d7d6d734480fe8acc6752c2.css): Permission denied in /home/myrestor/public_html/includes/file.inc on line 481.

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etc

I'm upgradign from 6.x to 7.9, everything went smoothly until i had to run the update.php.
I got the message

PDO is required!

Drupal 7 requires PHP 5.2.4 or higher with the PHP Data Objects (PDO) extension enabled.

See the system requirements page for more information.

I asked to host and got assured that PHP Version 5.3.8 and PDO - PDO drivers : sqlite, sqlite2, mysql.
What else can i do to make it work?
Any help appreciated!
Thanks!

Currently I am using Drupal 6. I look into the modules I use in drupal 6 and found out the following module not yet supported in drupal 7:

I need to rewrite this D6 code to D7.
I can't sort out how to write it correctly.
Can anyone help me out?

Apologies if slightly off topic but --
I host a site which was in some ways foistered on me.
It's running 6.22 uses a shed load of modules and is based on the acquia theme.
We have lost the original developer and my role is simply to keep the lights on.
I'm very worried that in upgrading a module the site might no longer work exactly as it is supposed to, things are never as backwardly compatible as you would like, and often for good reason.
So to the question, with Drupal 8 in the offing how long can I keep it on 6 before I have to move it to 7?