First thing, and I say this every time someone asks for advice on the internet - please, I beg you, get a real live human being in person teacher. We all need the money, and there are so many large and small elements of playing that take 5 minutes in a lesson, and take enormous effort to clarify in writing. I get it - it may be a difficult option for you depending on where you are and your resources of time and money. What can I say? However expensive lessons will be, an RSI is more expensive.
On double bass (upright, bull fiddle, dog house, I don’t care what you call it…), one starts with 1 on the ‘first fret’ (I know, there are no frets…), 2 on the second fret, 3+4 for the third fret. One of the big reasons for this is ergonomic support - 4 is your weakest finger, and I would strongly advise against ever fingering a note with just 4.
Same thing with an electric bass, or an acoustic ‘side bass’ (or whatever else you want to call the thing) - it’s less of a fuss whether you want to use the 1, 2, 3+4 or one finger per fret, and the scale length counts for a lot more, BUT - until you’re used to the instrument, I strongly advocate always making sure that the other three fingers are also down to support the fourth finger.
Also - where is your thumb? I strongly advise keeping it on the other side of the neck from your third finger, and keeping it parallel to the frets/perpendicular to the neck. ‘Hitchhiking’ (thumb parallel to the neck) is right out. (I make my beginning students wear a finger puppet on their thumb. As long as I can see Mr. Tiger, I know we’re good; if Mr. Tiger disappears, I know the thumb position is inefficient.) Thumb wrapping should be considered an advanced technique, and frankly, if your hand were big enough to thumb wrap, you wouldn’t be asking us this question.
Also your left elbow - it should hang in such a way as to give advantage to your fourth finger. It’s the weakest finger, the shortest finger, and it has the hardest stretch to get to the fourth string (lowest in pitch, closest to the ceiling). The elbow can help with all of that. And the elbow is going to provide you with the ability to shift up and down the neck easily, which you’re going to be doing a lot of.
Don’t be afraid to start at the ninth fret and slowly work your way down. The positions of your fourths and fifths are the same, and the frets are closer together. Nothing wrong with working out your I - vi - IV - V chords up there in oddball keys like Db/C#, Gb/F#, B, and E - it will serve you well as you go further down (lower in pitch, therefore down) the neck.
Pick vs. fingers - IDGAF, though I’d advise you to explore both. Geddy Lee uses fingers, Chris Squire used a pick, Tony Levin uses whatever he feels like using…