Buy an XP boost fro 7 days. The 7 day xp boost cost a little over 500 RP so its pretty cheap, and it gives the best value per dollar out of all the others.
Now the goal here is to play as many games as possible per day, and win them too. So, from levels 1-9 you should only play Coop VS. Beginner because from levels 1-9, coop vs beginner gives you just as much XP as a PvP game would.
The formula is xp =(3m)+25 . M is minutes played.
Once you're level 10, coop vs beginner gives you less xp. Now switch to coop vs Intermediate and play that until level 15. From levels 10-15, Coop vs Intermediate gives you just as much XP as a PvP game would.
The advantage of short bot-games is that you can easily fit them into your schedule even if you're busy. You can knock out a quick, 20 minute coop vs ai game in between college classes, homework assignments, in the morning before work, in the library with your laptop etc. If you go afk for 3 minutes to take out the trash, pick up laundry or get your pizza delivery, it won't cause you to lose. Though if you're afk for 5 minutes or more, your leaver level will rise.
Now, hopefully you made friends with some smurfs. Once you're level 16, coop vs ai gives reduced xp/ip. So it is time to do PvP.
For now, you should do only blindpick instead of draftpick, and here is why. You are required to have a champion pool of atleast 16 available champions (including freeweek champions) but even that is not enough. Player who spend more money on this game or are higher level than you are going to have a greater champion pool and will use that to counter-pick you.
So play blindpick with smurfs, stick to only a two to three champions that you're good at. Winning won't be as easy as you think since there will always be smurfs on the enemy team as well.
If the enemy team is bad or lacks smurfs, then instead of winning by 18 minutes, allow the game to drag out until 30 minutes.
Spend your ip wisely.
By the time you reach level 20, you will be able to buy tier 3 runes. To level up you don't need many champions so you should save your ip for runes. Only buy three 450 ip champions, and save the rest of your ip for tier 3 runes. You will definitely need runes for ranked.
If you have money, then you should buy the 7 runepage bundle, and one of the champion packs. Buying your champion pool or rune pages separately will cost a lot more RP than the bundles.