From (Mass Effect 1) Start of the Journey: Single Playthrough Builds (level 50 builds) by Simbacca:
Lvl 49 Vanguard
12 Pistols (Master)
00 Shotguns
08 Assault Training (Advanced)
07 Tactical Armor (unlocks Medium Armor)
08 Throw (Advanced)
12 Lift (Master)
06 Warp (Advanced)
07 Barrier (Advanced)
07 Singularity (Advanced)
12 Shock Trooper
08 Charm (12 at the end because of the 4 free points earned during the one playthrough)
04 Spectre Training (Basic)
Generally, what I do:
1. Start by putting points into available powers. I think Vanguard starts with 1 point in Throw and Warp, so I would put points into Singularity and Assault Training.
2. On my first level-up on Eden Prime (level 2), I would put 3 points into Charm/Intimidate. (You can do this first if you want, then put points into powers).
3. On the next level up (level 3) I would put 3 points into pistols for Basic Marksman.
4. You can finish Eden Prime at level 4, but you do not have enough points to get anything else to basic or advanced, so I would maybe save the points.
5. From there, on the Citadel, I would make a beeline to meet the council > track down Garrus (Chora's den > Dr. Michel's office) > recruit Wrex > go after Fist > rescue Tali > go to the council and become a Spectre. This will unlock 1 charm and 1 intimidate point and open up some more charm/intimidate pips in the talent tree.
I like doing that so you can put the 8 points in charm/intimidate as early as possible and get it out of the way. My level up strategy is to also try to get 1 point in all useful powers as soon as possible, so minimum Basic Barrier, Basic Lift, and Basic Shield Boost (armor) as soon as possible, while putting points into Charm/Intimidate.
I complete all the quests I can on the Citadel before leaving. A bunch require Charm/Intimidate for the best/easiest outcome so that is why I like having points available.
6. I then focus on my passive (Vanguard + specialization). The Rogue VI (Luna) mission unlocks at level 20. You can gain about 2-3 levels while completing Luna so you can save those points for when you get your specialization.
7. From there I like putting points into defensive powers, so armor and Barrier. Basically, I like being durable so I do not have to play the game like a cover shooter since the cover mechanics (and combat mechanics in general) can be rather clunky at times. Barrier and shield boost keep your shields up, and medium armor gives you more damage protection.
8. Then I would probably level up Pistols (Marksman) to improve your killing, followed by Singularity and Lift. You can always reverse that order if you prefer using powers over shooting, but Master Marksman really improves your killing speed.
If you care only about combat and do note care about passing most charm/intimidate checks (some charm/intimidate options are not really needed and are only there to increase your paragon/renegade score more quickly), you can ignore putting points into charm/intimidate and put them into your powers instead.
Regarding shotguns: while I like shotguns, I was never really good at using Carnage and never found it all that useful although I know other players really liked it. Maybe that is because I always tend to have Basic Carnage and never found it good, and even when I did have shotguns maxed I was always using Pistols (Master Marksman) or Assault Rifles on Shepard. On the Vanguard, I would just use shotguns as a mediocre backup weapon just in case. Soldier is probably a better shotgun user anyway since the soldier can unlock them with 4 points.
Vanguard is really good in Mass Effect 1, one of the best two classes in my opinion (the other is Infiltrator) but it takes longer to build up than say the Adept does.