Internet on phones wasn't that much later. I remember my sister had a slightly newer phone than me - I had the 3310 that everyone had with the swappable covers! She got the 3410 or something and it came with a free trial of WAP so she was on the wap internet all the time. No idea what this was 
I think just text-based forums??
But I remember being in the car feeling anxious when DS1 was tiny, that would have been 2009, and XP had the new iPhone 3G that could go online and marvelling that I could browse MN in the car to distract myself from his driving. That felt amazing - I guess I had no idea how much it would take over.
2007 though - I had this work at home freelance job answering questions on this service called AQA (any question answered) - you could text in which cost a POUND!! And get a reply back to any question. It was often people asking for directions, a phone number, or which takeaways were open, but you also got really interesting or random questions too. I loved it! It was so fun. I got paid about 20p for every question I answered and you had to try and pack as much info into 140 characters as possible without using text speak. It died a death in about 2010 because smartphones had really kicked off then and everyone had twitter. Looking back it's mad that people paid for stuff like ringtones and phone backgrounds? They were all listed in magazines and you could text to order them and they were so expensive.
Social media was very much in its infancy and I used it to connect with my actual friends only and it was a pain to upload photos because you had to get them off the camera or camera phone onto the computer with a card reader or USB cable, and then load up the website very slowly and load them on one by one. There are whole reams of photos I lost because I never transferred them onto a computer before the phone died. Also all phones had different chargers based on what brand they were, so if you ran out of charge and you hadn't brought yours with you you were completely out of luck.
Everything online was blogs and forums, it felt very personal and you could make strong connections with strangers. The internet felt like a completely different realm from "real life" - I think social media was the thing that changed that. I loved my computer, and was on it all the time playing Sims 2 or posting endlessly on forums, reading blogs. I learned about twitter from this ambulance driver blog I used to follow (he wrote a book - Blood, Sweat and Tea - it's great, you should read it) and when it first started, it was text message based - you texted your tweets in to a special phone number and it would connect to your account and post the tweet. The tweets of anyone you followed would then come through to your own phone. You couldn't do this today, it would drive you mad. But it worked (and was even quite nice!) back when you followed maybe 10-20 people and they all posted occasionally.