If you're buying your first electric guitar or amp, or purchasing a gift for someone new to guitar, this is a great place to start. There are so many options and lots of misleading info out there. I have no affiliations with any of the below. This is the advice I would give friends and family.
Do not buy of those $170-$220 starter packs. I'll say it again.... DO NOT buy one of those cheap starter packs. They seem like a great deal but I have yet to find one with an amp that has a reverb effect included. You have likely never heard an electric guitar without reverb on it (unless you have a friend with one of those cheap starter packs) and it does not sound good. What this means is you will immediately be looking for a replacement for that great deal on your amp or a reverb pedal and an extra cable because it won't have a pleasing tone and nobody wants to practice if their setup doesn't sound good. Your cheap starter pack just came with a $50-100 upgrade as a basic necessity. Good news is you don't have to break the bank. There are lots of good options for just slightly more than that.
*The one exception to the above is if you are purchasing for a small child who's just starting and can't comfortably hold a full sized guitar, the Fender Mini Squire Stratocaster pack is a great option. It includes a 3/4 scale guitar perfect for smaller hands. This varies by student but generally we'll say age of 9 and below. If this is your situation you can stop reading and pickup something like this in any color, as long as it says "3/4 scale".
**Personal note: if you're going to comparison shop on Sweetwater.com please consider buying directly from them. They’re a solid company that seems to treat their employees well, their return policies and customer service are unparalleled, and the price differences are hardly noticeable. Musiciansfriend.com is a great backup option as well. You can't go wrong with these two companies. Amazon has a lot of really below grade options that could prove more hassle than they're worth in small savings**
Here are my quick picks for amplifiers on a budget. Do not buy an amp without a reverb knob, a gain/overdrive/distortion option is great but not as necessary as reverb.
1: Fender Champion 20 1x8
Really great option for anyone looking for something for home use. Has all the standard features with a few extra bells and whistles. 8" speaker is the smallest I recommend and you can't beat the price.
2: Roland Cube -10GX
Similar features to the above. I prefer the sound to the fender reverb a bit more and the speaker sounds a little nicer. This amp gets a mention because of its super compact size while still having all the necessities.
3: Boss Katana 50
A bit more robust in features but also has a bigger learning curve to get good sounds. It does a bit of everything, which can be great for exploration, but isn't really amazing at any one sound. 12" speaker will give you some better bottom end if you plan to play in a group setting with friends at some point.
4: Fender Blues Jr III (or) IV
This is by far the best amp in this list. If you're able to spend a little more this amp could last you a lifetime. The majority of pro studios keep one on hand because they sound great at lower volumes are a super reliable. Link is to Reverb.com search because even a good deal used will cost you $350+. The III and IV have reverb, I & II do not.
Honorable Mention: This is not in the category of the amps above but this is my personal choice for a super portable practice amp that goes in my bag when I'm on the road for hotel practice.
5: Laney Lion Mini
Great set of features and doesn't sound bad for a tiny amp that can be battery powered. Plug in your phone for complete control of the effects via app or use it as is. Headphone jack for quiet practice times.
Guitars. Guitars. Guitars
Guitars have a much wider variety and rely much more on personal preference. The info below hopes to make it as low stress as possible.
Pickups Simplified - Any guitar from a reputable source will work for many things and there is no right or wrong
There are essentially two types of pickups for entry level guitars (the thing on the guitar that generates nearly all of the sound.) Single coils, like those found in Strat/Stratocaster style guitars and humbuckers found in Les Pauls & SGs. I would be roasted on a guitar forum for saying this, but for buying your first electric guitar those are your only two considerations.
Famous single coil players: Jimi Hendrix, Buddy Holly, Eric Clapton
Single coil sound: Associated with classic blues, soul, & R&B. Often described as bright/snappy - will have some buzz/hum in certain positions but this is partially what imparts the tonal qualities and is unavoidable.
Famous humbucker players: Jimmy Paige, Pete Townsend, Warren Haynes
Humbucker sound: Associated with classic rock, the heavier side of blues rock. Often described as smooth/creamy - increased sustain with overdriven or distorted sounds. Also, no hum/buzz, as the name suggests.
Single Coil Quick Picks:
1: Squire Bullet Strat - best bargain
Will get the job done, no worries on quality, pick any color you like.
2: Squire Affinity Series Strat - Recommend if you have a little more in the budget
Substantial jump in quality for a fairly modest price increase. Also available in a slew of colors.
Humbucker Quick Picks
1: Epiphone Les Paul Special - best bargain
Quality guitar that will last a very long time, lots of color options
2: Epiphone Les Paul Studio E1
Adds control of two tone and two volume knobs. Not a necessity but gives a better control of the tones.
If you're still with me, congrats! You just learned a whole lot and likely saved yourself a lot of time of sales people talking your ear off and trying to upsell you. Thanks for reading and I look forward to hearing you behind your new electric guitar soon!