If you have a 20 minutes to cook and few hours to wait , I whole-heartedly suggest you make your own ricotta.  It's surprisingly easy, inexpensive, and it yields the tastiest ricotta cheesecake.  I won't get into the details of how to make ricotta here, but I can recommend this guide from The Kitchn if you're new to the process.  You can see my own efforts from a double-batch in the image below.

To make enough ricotta for this recipe, you'll need about 2 liters (1/2 gallon) of whole milk, a few lemons, and some kind of setup to allow you to drain the finished product.  Because you want to heat but not boil the milk, many guides will tell you that you need a thermometer, but I don't think they're strictly necessary.  You want to turn the heat off after the milk has gotten foamy and is just starting to roll/simmer a bit more aggressively.  If you have an electric heating element, be sure to move the pot off of it right away.

If you're not interested in making your own ricotta, store-bought will do just fine - with a few very important caveats.  When baking with store-bought ricotta, you want to check the ingredients for binding agents like xanthan gum.  These binders help to hold together the ricotta on the shelf, but they don't play nicely when the ricotta is baked. Cheesecake made with binder-containing ricotta can turn into a weepy, crumbly,  disappointing mess.

You can use a low-fat ricotta if you want, but because ricotta is already very low in fat, the low-fat versions really aren't only minimally different anyway.

It's also worth noting that most store-bought ricotta includes added salt.  It's not usually all that much, but you may want to reduce or omit the salt called for in the cheesecake recipe in order to balance this out.

Two cheeses, both alike in dignity,
In fair Cheesecake, where we lay our scene...

With all apologies to Shakespeare, the schism between these two cheeses is perhaps a little over-wrought.  As with other recipes, opinions about Old World vs. New World ingredients can get a bit testy.  Whether you go with mascarpone or cream cheese, you're aiming to add flavour and richness to the ricotta, and to give the finished cake a more luxurious texture.  Both cheeses work beautifully in this respect, albeit in different ways.  I'm not going to concern myself too much with notions of authenticity - instead, let's just talk about what each cheese brings to this cheesecake.

Cream Cheese

Cream cheese has a unique and distinctively tangy taste that's front-and-center in New York style cheesecakes, and other American-style cheesecakes.  This is a pro if that's the flavour you're after, and a con if you're looking for something more neutral.  Cream cheese is difficult to blend entirely into cake batter, and will often leave behind small chunks.

Cream cheese is generally quite easy to find, and comparatively inexpensive, which is one of its biggest advantages.  While cream cheese is fairly rich, it is lower in fat, carbohydrates, and calories than mascarpone.

Mascarpone

A rich and wonderfully smooth Italian cheese, mascarpone is much more neutral tasting than cream cheese, and so are cheesecakes made with it.  It incorporates into the batter much more easily than cream cheese, and tends to yield a more uniform texture in the finished product.  Cheesecake made with mascarpone lacks the distinctive tangy taste of cream cheese, which may or may not be what you're looking for.  Mascarpone tends to yield a cheese cake that has a softer, cakey texture.

In North America, mascarpone cheese can be hard to find, and is generally much more expensive than cream cheese.  Mascarpone is higher in fat, carbohydrates, and calories than cream cheese.

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My taste-testers had decidedly mixed preferences for the two cakes.  Fans of tangy cheesecake were generally happiest with the cream cheese version.  Those who preferred a softer, more cake-like experience preferred the mascarpone version.

Long story short: if you want an Old World style cheesecake, go with mascarpone.  If you want something closer to (but definitely not identical to) an American cheesecake, go with cream cheese.  If you can't decide... make both.

Correct. No hot water bath. Unless you want one, that is.

Hot water baths help cheesecakes cook evenly, reducing the risk of cracking and the degree of browning.  But in this case we actually want more browning, as it helps the cake develop a flavourful pseudo-crust.  Cracking might be an issue, but there are a couple of points to consider here:

1. You're going to cover this with blueberry sauce.  Blueberry sauce hides all sins.
2. You can, weirdly, control/disguise the cracks to a degree.  Dragging a knife through the unbaked top to decorate creates blueberry-line-break-points that tend to corral any cracks.  You can see this in the photo at the very bottom of the post.
3. They're just cracks.  Cracked cheesecake doesn't taste any different.

Now, you absolutely COULD use a hot water bath to make this cake.  There's nothing stopping you.  You would have to adjust your baking time, but if you've made cheesecakes in this fashion before it won't be any different than what you're already used to.  The usual caveats about carefully wrapping the pan with tinfoil and avoiding leaks all still apply of course, so proceed with caution.

I personally wouldn't bother with the hot water bath for a crustless ricotta cheesecake, regardless of my ability to bury imperfections under sauces.  I like the browned edges, the cakey texture, and the overall simplicity.  However, if you were thinking about adding a crust to this recipe (see Variations below), then I'd consider making the adjustment.  If you do try this with a hot water bath, I'd love to hear how it goes!

In this section I'm going to take a little space to talk about some potential variations that you can try out with this recipe. If you've jumped ahead to this section looking for information about using cream cheese vs. mascarpone, scroll back up a little to the notes to the previous sections.

I adore blueberry and lemon, but there are plenty of fruit options you could try out with little difficulty.  If you're working with fruits that, like blueberries, produces a fair bit of liquid when they cook, you can generally make a straight substitution.  If you don't want to use lemon (or another citrus) juice, you can swap it out for water instead.

Sour cherries would be fantastic choice here.  I tend to think they'd be best with the cream cheese variation, but that might just be a product of bias, given how often cherries show up on New York cheesecakes.  Raspberries would also be excellent.  If you have access to them, blackcurrants would be phenomenal and very distinctive, though you may need to sweeten them a bit more than some other fruits.

Want get super simple? Omit the fruit entirely!  Cheesecake purists around the world will tell you that a cake needs to stand up on its own merits, and I truly do believe this base recipe does just that.  However, if you do decide to make changes, don't underestimate the impact of the lemon.  The juice adds acidity and some flavour, but the zest actually contributes some pretty big flavour notes.  There's nothing wrong with dropping that component if it works for you, but do take into account the overall shift in flavour profile.  Completely plain cheesecake can be, well, a bit plain.

Want to add a crust? As long as you've got some experience with cheesecake crust, then I say go for it!  Any graham cracker, cookie, or nut-based crust would be lovely.  You can use pretty much any recipe that you like, and I don't believe you're going to need to modify the cooking time all that much, though you may want to opt for a hot water bath cooking method instead (see Recipe Notes above for more on this subject).  If you're looking for something that would play off of the blueberry and lemon in particular, I suggest trying a hazelnut crust.  I haven't got one to recommend myself, but if you have one that you love, please let me know in the comments!

Keep in mind that any crust you add will change the nutritional profile of the finished dessert.  Needless to say, if you use Graham crackers or any other wheat-based biscuit, the recipe will no longer be gluten-free.