Reddit mentions of Devi Ever Shoe Gazer Muffy Fuzz

I'm going to do my best to help but without a given budget it's a little more difficult, though I'm going to assume a sub-$150 range seeing as though it's a gift. While there are not a lot of particular pedals made exclusively for shoegaze, there is a pretty agreed upon category of effects to give the shoegaze sound: fuzz/distorition, delay, reverb, modulation.

Fuzz: My personal favorite category

Electro Harmonix Big Muff Pi- there are a lot of different variations of this pedal, many in the boutique market (read: price range), but the newly launched Nano Big Muff is a great compromise of sound and space.
Devi Ever Shoegazer- a little more pricey, but if you peruse the used markets you can occasionally find one for a little less than $150.
Way Huge Swollen Pickle- A Big Muff variation, but with a lot of additional controls to help sculpt the sound you want. There is also a newer version that moves the original SP's internal trim pots to the outside.
Blackout Effectors Musket- Yet another Big Muff variation, but my personal favorite and the one that currently presides on my board with very little risk of being replaced any time soon.

Distorition

Proco Rat- A fun little distortion pedal that's capable of some huge sounds
Dr. Scientist The Elements- A little more pricey, but arguably the most versatile distortion on the market, capable of everything from a clean boost to massive, almost fuzz-like distortion.
Walrus Audio Iron Horse- only slightly over budget, but a great distortion

Modulation

Chorus- A few suggestions for a classic shoegaze effect in ascending price:
EHX Small Stone
MXR Analog Chorus
TC Electronic Corona Chorus

Tremolo- The other classic shoegaze modulation effect
Boss TR-2
Voodoo Lab Tremolo
Fulltone ST-1 Supa-Trem
Mooer Trelicopter- Haven't tried this one and there's mixed reviews about the Mooer's quality control, but from what I've gathered, this isn't one of the pedals people seem to be having lots of issues with

Delay

TC Electronic Flashback- Also available in the X4 model (larger but offers presets)
Boss DD-3- Really any of the Boss DD series pedals would do the trick, and they go for a steal on the used market
EarthQuaker Devices Dispatch Master- a combo delay and reverb that sacrifices versatility in exchange for an awesome sound
MXR Carbon Copy- an extremely popular delay on this sub. This one's analog as opposed to digital, meaning the repeats will be a little darker, but the available modulation for the repeats sounds really good.
Malekko 616 Delay- Another analog delay that's fairly comparable to the Carbon Copy, but this pedal offers adjustable modulation amounts.

Reverb

TC Electronic Hall of Fame- My current favorite reverb pedal! Offers a wide variety of sounds, each with a fair amount of control, but the toneprint ability is really where this pedal shines.
Neunaber WET
Electro Harmonix Cathedral- a little pricer, but a great reverb with cool features like reverse reverb and a hold switch
Digitech Digiverb- There's a bit of a split consensus on this pedal, as some think its terrible and some love it. That being said, you can regularly find these things on the used market for around $40. If you went for a cheaper fuzz option, you could pick up one of these used for the reverse reverb setting alone- placed before a fuzz, it perfectly hits that huge Kevin-Shields sound.

These are just a few suggestions since I don't have too much time to keep going at the moment, but feel free to reply or shoot me a PM if you have any questions or would like more suggestions and I'll do my best to get back to you by tonight.