As a beginner, play everyone on rotation in bot match. Your primary goal is to learn enough about every champ that you understand what that champ does when you face off against it. Your secondary goal is to find if a champ "clicks" for you, and if it does, make a note of it as someone you'll save BE for. (And don't be prejudiced based on appearance or reputation: a champ I thought was worthless because of how badly I'd seen it played in my games I tried on rotation just to see why it was so awful—I hit the Mastery 4 cap in as many days and have mained it through a few thousand matches.)
Only use bot match to break-in the first or second time out with a champ before going to normals. Bot match gives you a moving target that will at least fire back, but bots don't behave like players and will train you in bad habits if you use botmatch for anything beyond you learning to pilot the champ and throw its skills around.
Regarding investing in champs, I suggest that you pile up shards and rely on rotation early, and not disenchant till you have 2+ or try the champ on rotation and decide that you're not interested in it. I dusted a few champ shards that I soon wished that I hadn't for champs that I quickly regretted unlocking. Basically, the shard is worth 20% of the champ's BE cost when disenchanted, but the shard pays for 40% when used to unlock, so you're saving up to 1260♦ by using shards to unlock when you can.
How to get better? There are two kinds of learning, I find, in this game.
First is the "tip". Things like "put a ward in this bush" or "ping botlane if you're mid and your enemy goes for a walk southward" or "if the enemy jungler is attacking toplane, you perhaps can take one of his camps or sneak the drake" are all little things that everybody needs to have in mind. The second is the "nuance", which are the things that mostly are learned by experience. I can explain in text, and others (much better) have in videos on YT, how minion waves can be manipulated to accomplish certain goals, but it's all words till you spend time experiencing it, and most importantly, they can't be boiled down to become a "tip" because there are too many exceptions or other factors involved for a rule of thumb form to work more often than it fails. Lots of bad play in low elo is people doing "tip" forms of "nuance" situations, like they get three kills, lose one player, and despite having a health and manpower advantage for 30 seconds, everyone is backing or farming an outside wave when they should be rushing Baron or drake or grouping to push down a mid turret. This is because of a lack of a shot-caller, and everyone having a vague idea of what things they can do (farming = good, right? Spending gold for a power spike > it rattling in your purse, right?) and scattering to do their own thing rather than realize that at that point in the game, The Team is its own creature and behaves differently than its constituent champions do individually.
Tips you can pick up and implement easily, so integrate them into your play as they come. Nuanced behaviors must be practiced. For example, take an ADC, say, Jinx, botlane and set your goal to manage the wave, learning how to use her Q toggle and E properly to ensure that you can freeze when you want, push when you want, and not miss much CS or any (reasonable) siege minions. Two or three games like that and you'll be able to push that experience into your subconscious where it can become a habit (like "riding a bicycle") and then you can task your conscious with a new goal (like, bring a hook/engage support and practice landing the chompers to chain CC and focus down an enemy when they overextend) while still honing the previous goal passively (because you'll start to feel your mistakes, like, "I wish the wave wasn't pushed up quite this far and that I had more mana, I must've used too much fishbones when I was worried about missing CS on that last wave," and you'll fine-tune automatically) and in that way you can build proficiency.
